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Certain Properties of Fractional Differential Variation Function |
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PP: 425-433 |
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doi:10.18576/pfda/120211
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Author(s) |
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Sudhir Kumar,
Jyotindra Prajapati,
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Abstract |
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| Prajapati and Kachhia introduced the concept of functions of bounded fractional differential variation and posed an open question: ”Is the class of functions of bounded fractional differential variation on a closed bounded interval a Banach algebra?” The authors provided a solution to this problem in their previous work titled ”Functions of bounded fractional differential variation: A new Banach algebra”. This paper continues the work initiated in the aforementioned article. In this study, the authors define a fractional differential variation function for a function f in the space BFDV[a, b]. Additionally, we discuss several inequalities within BFDV[a, b], which are utilized to explore various properties of the fractional differential variation function that are inherited from the Caputo fractional derivative of its parent function. |
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