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02- Progress in Fractional Differentiation and Applications
An International Journal
For Authors

Manuscript Preparation

To find information regarding our standard peer-review practices, please consult the Editorial Policies and Practices; otherwise, the following guidelines provide an overview of content, technical, and style requirements for preparing manuscripts for submission to the NSP journals.

Content Guidelines

Readability and Accessibility: Take special care to ensure that manuscripts are well organized, clearly written in scientific English, and written in a style consistent with that of the NSP journals. It is not possible for editors to undertake extensive corrections of manuscripts, due to time constraints and the risk that the authors’ meaning might be distorted. If your first language is not English, consider seeking help from a native English speaker when writing your manuscript.

Direct the manuscript text at a general readership, so as to make it understandable to a broad spectrum of researchers. NSP editors recommend avoiding jargon and the excessive use of acronyms, even for commonly used terms. If jargon and acronyms are necessary, please define them in the text. Also, avoid the introduction of new terminology except when needed to convey a unique or nuanced meaning.

To enhance readability, display all but the simplest equations, rather than including them as inline text. Format figures and tables such that their content and details are readable when they are sized for the journal page. The size of the smallest capital letters and numerals should be at least 2 mm.

NSP editors ask authors to proofread papers prior to submission, to eliminate grammatical errors, misspellings, and omission of symbols.

General Content: Clearly states the relation of the submitted manuscript to previously published work, including papers, meeting abstracts, and conference proceedings. (Preprints and internal laboratory reports are not considered publications.) If the results reported in the manuscript correct, supplement, or supersede previous results, state this advance. Distinguish your results from those previously obtained.

The NSP journals require authors to abide by the length guidelines. An automatic count of the length of each manuscript is made upon submission. If this count indicates that the manuscript’s length exceeds the journal’s limit, staff will more carefully calculate the length. Authors will be asked to shorten over length manuscripts prior to review. The length restriction applies to all versions of a manuscript. Upon acceptance for publication, the length of a manuscript may be re-evaluated and cuts may be requested prior to production. More edits may be necessary when the article is composed into journal pages; this process may cause a delay in publication of the article.


Titles should be concise and informative, clearly stating the main findings of the manuscript. Avoid using new terminology, hyperboles assessing the quality of the work (“precise,” “important,” or “accurate”), proper nouns and brand names (name of equipment, people, or places), and coined words. Titles of manuscripts submitted to the Comments section have the format ‘Comment on “Title of the original paper”.’


Abstracts should concisely summarize the subjects, conclusions, and results of the manuscript. In the abstracts of experimental papers, specify the quantities measured and objects studied and clearly describe the experimental conditions. Avoid coined words and unexplained acronyms. Abstracts should be self-contained and should not include footnotes or citations to references, as abstracts are reprinted in abstracting journals and databases where such information is not useful. Note that Comments and Replies submitted to NSP do not require abstracts.

Supplemental Material

Supplemental Material is information that is useful to a subset of readers but is not essential to comprehend the article’s main results. The NSP journals archive Supplemental Material, providing permanent access to the information. Supplemental Material includes, but is not limited to, multimedia files, tables of raw or analyzed data, parameters used in or produced by calculations, and computer codes. Information regarding how the research was conducted, such as details of sample preparation, and derivations of equations, can also be included in the Supplemental Material if this information is not crucial to a reader’s understanding of the associated paper. The paper must stand on its own; it must be understandable and convincing without the Supplemental Material.

Supplemental Material is subject to the same copyright agreement as the associated paper. Follow the guidelines in the copyright agreement for the published manuscript when replicating information included in the Supplemental Material.

Do not use Supplemental Material to avoid a length limit; often, a short paper accompanied by a lengthy supplement is not appropriate. Editors use their judgment to decide if a longer manuscript with all material integrated into the main text is required. The editors may seek guidance in this decision from the referees who review the manuscript and Supplemental Material. In a longer format manuscript, it may be best to present additional material as an appendix to the main article, rather than as Supplemental Material. In general, Supplemental Material should not accompany Comments, Replies, or Errata. List all references cited in the Supplemental Material in the main text.

Cite the manuscript’s Supplemental Material in the reference list as follows:

See Supplemental Material at [URL will be inserted by publisher] for [give brief description of material]. All files related to a published paper are stored as a single deposit and assigned a Supplemental Material URL. This URL appears in the article’s reference list.

Technical Format and Style Guidelines

References and footnotes

Combine references and footnotes to text material in a single list, and number the items consecutively in the order in which they are cited. Designate references and footnotes in the text with inline numerals in square brackets.

NSP journal allows footnotes to appear separately from references. Footnotes are placed at the bottom of the page on which they are cited. They are designated with superscript numbers and numbered consecutively throughout the paper. Footnotes within tables should be designated with lower-case letter superscripts and given at the end of the table.

When citations are made to internal reports, other items not available in the published literature, or unpublished work, it is the responsibility of the author to provide sufficient information to enable the reader to obtain a copy of the cited material. Citations to papers published in peer-reviewed journals are considered primary references. Citations to e-print archives should not be used in place of primary references. Citations to classified reports or other documents with restricted circulation should be avoided. All citations, including those cited in figure and table captions, should be listed in the reference section.

It is important to confirm the accuracy of the bibliographic information in the references. Links will be added to the cited document. If reference citations are incorrect or incomplete (e.g., missing author name, or an incorrect volume number or page), the associated links may fail.

NSP encourages authors to include titles for all references as an aid to the reader. If this format is used, it must be applied to all references. 

Byline and Affiliations

Bylines: The names of authors and their professional affiliations must be given in the byline at the beginning of a manuscript. If the number of authors exceeds 40, the authors will be listed in the Table of Contents as, e.g., A. Jones et al. The author who submits the manuscript is responsible for ensuring that all listed authors approve the inclusion of their names, and for checking that each name is written in the format normally used by that author.

Formatting A Collaboration Author List: Collaborations of 50 or more authors are encouraged to use the SPIRES Collaboration Author Lists XML Format to submit author names. Please provide the ‘authors.xml file’ when submitting the manuscript.

Collaborations may also use a TeX format for author names. In that case, use Latex for the text file, not Word or plain LaTeX, and name the files with a ‘.tex’ extension. To automatically link author names with affiliations, use the REVTeX 4 “superscriptaddress” document style as described in the Latex Sample. Please include the author list in the main text file of the submission (the one with the \begin{document} command). List each author on a different line and use the “\author” command. Only use standard LaTeX and REVTeX 4 commands in the author list. Completely remove collaboration members from the author list that are not to be listed as authors on the manuscript.

Affiliations of authors should be given without abbreviation. (Use Massachusetts Institute of Technology, not MIT.) Give the city, state, and zip code; add the country for other addresses. Affiliations must be institutions, not conferences, collaborations, or temporary meeting places.

If the authors are at different institutions, author names may be grouped by institution with the name of the institution following each group. If the authors are not grouped by institution, the names of institutions may be presented in a single list following the list of authors. A variant form for listing institutions links each author to their institution(s) unambiguously via a superscript numeral: Each institution is given a number, and the relevant number is then placed after each author’s name. Group (collaboration) names can be listed in addition to author names. The group name goes in parentheses after the list of authors and before the list of institutions. Please choose the most concise presentation.

Footnotes to an author’s name or address facilitate locating or communicating with an author. In many cases, it is helpful to identify an author as “spokesperson” or “author to whom correspondence should be addressed.” Footnotes giving email addresses of one or more corresponding authors are encouraged. Along with email addresses, authors are also encouraged to add their preferred pronouns (he/him/his, she/her/hers and they/them/theirs). Include information concerning research support in the acknowledgments. Footnotes describing an author’s position or title are not acceptable.

Place information concerning author contributions, such as statements of equal contributions, in a paragraph after the Acknowledgment section. For example, “A.B. and C.D. contributed equally to this work.” or “A.Z. and B.Y. conceptualized the work; C.X. conducted the experiments.”


Acknowledgments are a simple statement of thanks that appears at the end of a manuscript. They can recognize named individuals who contributed scientifically to the research of the paper; cite the funding agencies that provided financial support for the work; and note the affiliation of institutions in the byline. Acknowledgments to people precede those of financial support.

Acknowledgments may not recognize those who helped in preparing the paper; editors who handled the peer review of the paper; those who contributed general encouragement (family, friends); or those who provided services that were not directly part of the research. Acknowledgements may not include a dedication or a memorial.

Acknowledge positions, titles, and awards only if they provided funding for the research and state the source of financial funding in such cases. Noting the date associated with an award is not appropriate.

Notations and Mathematical Material

Keep notation clear, compact, and consistent with standard usage.

Neatly format, punctuate, and align equations to bring out their structure. Number equations on the right. Punctuate mathematical expressions and displayed equations as part of the sentence. Use single-letter symbols for mathematical quantities in equations and expressions, with subscript or superscript indices or labels, if necessary. Replace a frequently repeated mathematical equation with a symbol. Use bracketing as necessary to ensure clarity. Note that the solidus (/) in fractions, for example 1/2a, means 1/(2a) and not (1/2)a. Do not use a center dot to indicate multiplication except for products of vectors, dyadics, and the like.

In general, three-vectors are set in roman boldface. Four or more vectors are usually set in lightface italic, but boldface is acceptable. Ordinary type is preferable when using Greek letters. Typographically distinguish matrices, operators, and other general quantities only to avoid confusion; in such cases use boldface or a caret.

Tables and Figures

Tables are numbered (with roman numerals) in the order in which they appear in text. Give each table a caption that explains the contents of the table and that includes definition of symbols. Keep column headings simple and include units in these headings. Very simple and brief tabular material may appear in the text without a number or caption.

Use a single horizontal rule to separate the column headings from the entries in the table. Use horizontal space within the body of the table to separate broad groups of entries. Extra vertical space may be used between columns. Avoid vertical rules in tables. Use lower-case roman letters for footnotes placed at the bottom of a table.

If space allows, long data tables can be included directly in the manuscript, rather than in the Supplemental Material. This decision is influenced by whether readers can accurately obtain the data from a figure and by how many readers are likely to use the numbers. If experimental results are likely to be used as reference values by other authors, publication of the numbers is desirable. Extensive datasets may be deposited as Supplemental Material. If additional numerical data are available, include a statement regarding the availability of the data at the end of the manuscript, before the Acknowledgments. The statement should cite a reference that provides the information needed to access the data (e.g., name of repository, doi, etc.).

Figures should have a width of a 8.6 cm or 3 3/8 in, the width of a single manuscript column. Use a width of 1.5 or 2 columns for more detailed figures. Authors are required to submit all figures electronically for production. Preferred formats are .ps, .eps, .pdf, .jpg, and .png; refer to the manuscript Submission Guidelines below for more details. Number figures in the order in which they are referred to in the text.

Give each figure a caption that clearly summarizes the contents of the figure. Define figure symbols and curves either in a legend in the figure itself or in the caption. Label subfigures (a), (b), etc., and include a description of each panel given in the caption. If possible, submit figures with multiple panels as one file.

Format figures such that their content and details are readable when they are sized for the journal page. Make the height of the smallest capital letters and numerals at least 2 mm and make the diameter of each data point at least 1 mm. Make a curve’s linewidth at least 0.18 mm (0.5 point). Avoid small open symbols, shading, and cross-hatching in figures.

Submit photographic images (either grayscale or color) as high-resolution .jpg or .png files. Avoid submitting prescreened (scanned) images of photographic material as they may not have sufficient resolution. If scanned images have to be used, make scans with as high a resolution as possible (preferably 600 dpi or higher) and then scale the figure to its final size.

Figures should accurately present the scientific results. If adjustments to images, such as changing its brightness, are made, state the adjustment in the figure caption.

For color-online-only figures, a .ps or .eps file is required for production. Ensure color online figures are intelligible in grey scale. To achieve this goal, use colors that have clearly distinguished grey-scale values. To assist in differentiating colored curves, use different line styles (dashed, solid, etc.) and give a description of the lines in the caption. If colored figures are desired in the print version of the journal, as in the online version, clearly indicate which figures are intended to be printed in color when the manuscript is submitted.

In order to reproduce previously published figures, tables, etc., authors must show that they have complied with the requirements of the publisher of that material. Authors can demonstrate they have permission to reproduce the material by sending a written agreement from the publisher and author of the originally published work. If the original journal is published by APS, only a written agreement from the original author is required.

Manuscript Submission and Resubmission


Submit manuscripts via our Submissions server. The Submissions server is designed to enable fast and easy uploading of the manuscript and to enable entering of information required for the peer-review process. Receipt of a submission during business hours is acknowledged by email within one business day.

Specify the author to whom correspondence should be addressed, and give all available contact information for this individual (postal and email addresses, phone number).

Submissions formatted in Latex or MS WORD are preferred. Upload the main body of the manuscript (including figures, tables, captions, etc.) to the Submissions server as a single file. Also send a cover letter, auxiliary files and figures, and Supplemental Material via the Submissions server. Copies of the manuscript sent by regular mail are not processed.

Authors of manuscripts that are sent for external review are directed, via email, to an online, interactive service to complete the needed “publication rights” agreement, such as the APS Transfer of Copyright agreement. While the agreement takes effect only when the manuscript is accepted for publication in a NSP journal, the prompt completion of this process prevents unnecessary processing delays. Accepted manuscripts are not forwarded to production until the journal is in receipt of the agreement.


When resubmitting a manuscript, please include a summary of changes made and a concise, point-by-point response to all recommendations and criticisms. The modified manuscript and figures can be uploaded using the interactive resubmission forms available on our Submissions server. These forms should also be used when a manuscript previously submitted to one NSP journal is transferred to another. Send the complete text file if there have been any changes.

For any resubmission, please state whether or not the figures have been modified, and supply new electronic figures if there have been changes. It is only necessary to resend figure files when the previous versions are no longer valid. Please update any other information (e.g., address and contact information) that has changed since the initial submission.

Author Inquiries

If clarification is needed, send an email message to the journal with the following subject line: Status, Manuscript ID, and Corresponding Author Name.

For accepted papers, information about the production status is available via a similar service maintained by the production vendor. A link to this service is provided on the manuscript status page.

Review Process

The following information provides details regarding the review process for manuscripts submitted to the NSP journals.

Peer Review: Peer review by independent, anonymous referees is one of the most important reasons for the existence of a scientific journal. Journal readers benefit since at least one independent expert has judged that the manuscript is new and interesting, that it contributes to the advancement of the field, and that it is without apparent flaws. Of course, it is impossible for either the journal or the referees to guarantee the correctness or the originality of the research. Authors benefit from peer review via feedback on the research and the style of presentation. Note that the review policies and procedures vary by journal.

Review Timeline: The time from receipt to publication of a manuscript depends on many factors, including the article type (Letter or Regular Article, for example), the availability of referees, and the editor’s workload. The time authors take to respond to referee comments and revise the manuscript also plays a role in the review timeline.

Referee Selection: Editors choose one or more referees from a common database of thousands of potential referees. The editors base their referee choices on factors including the referee’s area of expertise and their availability (we try to avoid overburdening referees), the quality of the referee’s reports, and the referee’s typical response time.

Suggesting Referees: Authors are encouraged to suggest the names of potential referees. Referee suggestions can be added during the manuscript submission process on the Editorial Info page. Click on the “Add” button and enter the name, email, and affiliation for each suggested referee. The editors consider the suggestions, but the suggested referees are not necessarily chosen. Authors should avoid listing previous coauthors and collaborators.

Excluding Referees: Authors can request that certain referees are not contacted. The names of these referees can be added during the manuscript submission process on the Editorial Info page. In the text box, provide the names of a few specific people (not names of research groups, collaborations, or institutions) and include a brief explanation of why you are making the request. Although such requests are usually honored it is customary to give authors whose work is criticized in a manuscript an opportunity to respond to the criticism.

Number of Referees: The number of referees contacted to review a manuscript varies by journal. Typically, editors choose one or two referees to initially review a manuscript. In some cases, the editors may contact more than two referees, for example to gain input from referees with differing expertise or if there is uncertainty about the availability of a particular expert. If a referee is tardy, the editors may contact an additional referee, and if the tardy referee then responds, we may receive more anonymous reports than usual. If an impasse is reached between the authors and referees, the editors may consult another referee in an effort to close the review process.

Rejection without Review: Not all manuscripts are sent for review. Editors often reject manuscripts that they judge to be clearly unsuitable for the journal. However, no manuscript is accepted for publication without review by external referees.

Rounds of Review: Editors typically reach a final decision on whether to publish a manuscript after one or two rounds of review.

Responding to Referee Reports: Authors should read referee reports carefully and dispassionately and approach the reports with an open mind. What may at first seem like a devastating blow is perhaps a request for more information or for a more detailed explanation. At other times the referee may indeed have found a fatal flaw in the research or logic. Put yourself in the position of a reader, which is exactly the position of the referee. Is the manuscript well written? Is the presentation clear, unambiguous, and logical? Respond to all referee comments, suggestions, and criticisms. When writing your response, please formulate it in gender-neutral terms. If unavoidable, please use the singular “they/them/theirs” in place of gender-specific pronouns. Explain which changes have been made and state your position on points of disagreement..

Post Acceptance

If your paper is accepted for publication in a NSP journal, please consider submitting a summary of the paper. The summary should include a newspaper-style headline and one paragraph explaining the main result of the paper and why it’s important. Write the summary so that it’s understandable by non-scientists. Send the plain text summary (no LaTeX or Word documents) to nsp@natural-s-publishing.com with the subject line “summary [accession code]”. When emailing the summary, consider sending one or a few low-resolution image files that illustrate the results. Preferred formats are jpeg/jpg, gif, and png. After a summary is submitted, an automatic email acknowledgment will be sent from NSP email.

In addition, the NSP editors occasionally consider summaries when making decisions on what papers to highlight as Editors’ Suggestions. These papers are judged to be particularly important, interesting, or well written, and are prominently displayed on the journal web pages.

Hints for Writing a Good Summary: Be brief. 200 words is usually enough. Shorter summaries are often better as they include fewer details that tend to distract from the main points. Try to get to the “bottom line” in the first sentence or two before stepping back to go over background information. Think of the way a newspaper article is written, with the most important points at the top. Aim the summary at non-scientists and not technology. Using this style helps those reading the summary to visualize how the topic could be presented to a non-scientific audience. Avoid or define any jargon. State why the result is important in direct terms, even if it seems obvious. Clearly distinguish between what is new in the paper and what is merely background information.

Other Publicity: The journal editors encourage authors to notify their institution’s public information or press office if the paper is accepted. The press office may want to mention the paper in their own publications or may want to inform local media.

Publication Charges and Reprints

The NSP journals provide authors with an online, to pay for various author charges, including applicable publication charges, and reprints.

Color Figures Charges: Color illustrations in the print journal should be used only when there is a clear need. The additional costs for printing illustrations are borne in full by authors and their institutions. Authors are reminded that Color Figures Online Only is a service provided in NSP journals without charge to authors.

Authors desiring color in print, who are willing and able to pay the associated charges, should indicate their request, preferably upon submission, and indicate which figures are intended for color in print. Full payment of the color charges is required before the article is sent to production. If payment is not received within 21 working days, the article is sent to production with the figures designated as color online only, provided those figures have been properly prepared as individual electronic files (color online only results in no charges to the author). If authors require more time to pay the charges, the article will be held until the anticipated payment date.

Reprints: Authors can order reprints and obtain associated prices. For authors’ convenience and to minimize delay, NSP accepts payment by major credit card. For those who require invoices to make payment, the system offers this option as well. Please note that reprints are created and mailed after the journal issue has been printed.

Open Access Publishing Options

The NSP offers some of the most-trusted, most-read, most-cited, and fastest-growing fully open access and hybrid journals and related areas of research. Both fully open access journals and hybrid journals allow authors to publish their research immediately open access, usually upon payment of an article publication charge (APC).

NSP journals allow authors to publish at no cost under the traditional subscription model, and also provide authors the option to publish an accepted article open access under a CC-BY 4.0 International license, upon the payment of an APC.

CC-BY 4.0 International is one of the most permissive Creative Commons Attribution licenses available and permits anyone to copy, distribute, transmit, and adapt work with proper attribution. Authors retain copyright to their articles under this license. Authors seeking to publish articles under the Creative Commons Attribution license should select this option when they are asked to complete the appropriate Publication Rights documentation. Accepted licensed articles will not be published until any applicable APC is paid in full.

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