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Limit-Residual Function Method: A New Approach to Creating a Power Series Solution for Fractional Differential Equations |
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PP: 491-505 |
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doi:10.18576/pfda/110305
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Author(s) |
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Aliaa Burqan,
Ahmad El-Ajou,
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Abstract |
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| This study develops and applies a new iterative scheme to generate analytical solutions for linear and nonlinear fractional differential equations. The solution methodology involves producing a fractional power series solution in the form of a rabidly convergent series using the concepts of the limit and the residual function without the need to transform the target equations into other spaces or calculate the derivative to determine the power series solution coefficients, which requires less computational effort than other approaches. This method can be an alternative to the residual power series method, which can be easily and efficiently used to deal with nonlinear fractional differential equations arising in various physical phenomena. To illustrate the procedure and validate the effectiveness of the suggested approach, several applications are studied. This enabled us to demonstrate the potential, accuracy, and the method’s versatility in dealing with these equations under restrictive constraints. The complete reliability and efficiency of the proposed algorithm are readily demonstrated by numerical results combined with graphical representations.
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