Generalization of Homotopy Analysis Method for q-Fractional Non-linear Differential Equations

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DOI: https://doi.org/10.28924/2291-8639-22-2024-22
Published: Jan 29, 2024
Cite as:
B. Madhavi, G. Suresh Kumar, S. Nagalakshmi, T. S. Rao, Generalization of Homotopy Analysis Method for q-Fractional Non-linear Differential Equations, Int. J. Anal. Appl., 22 (2024), 22.

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B. Madhavi, G. Suresh Kumar, S. Nagalakshmi, T. S. Rao

Abstract

This paper presents a generalization of the Homotopy analysis method (HAM) for finding the solutions of nonlinear q-fractional differential equations (q-FDEs). This method shows that the series solution in the case of generalized HAM is more likely to converge than that on HAM. In order that it is applicable to solve immensely non-linear problems and also address a few issues, such as the impact of varying the auxiliary parameter, auxiliary function, and auxiliary linear operator on the order of convergence of the method. The generalized HAM method is more accurate than the HAM.

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