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A new iterative method with \(\rho \)-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative

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Abstract

In this paper, the new iterative method with \(\rho \)-Laplace transform of getting the approximate solution of fractional differential equations was proposed with Caputo generalized fractional derivative. The effect of the various value of order \(\alpha \) and parameter \(\rho \) in the solution of certain well known fractional differential equation with Caputo generalized fractional derivative. Applications to the certain fractional differential equation in various systems demonstrate that the proposed method is more reliable and powerful. The graphical representations of the approximate analytic solutions of the fractional differential equations described by the Caputo generalized fractional derivative were provided and the nature of the achieved solution in terms of plots for distinct arbitrary order is captured.

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Acknowledgements

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa, Anand, Gujarat, 388421, India

    Nikita Bhangale & Krunal B. Kachhia

  2. Department of Engineering, Sciences and Humanities, Vishwakarma Institute of Technology, Bibwewadi, Pune, Maharashtra, 411037, India

    Nikita Bhangale

  3. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

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  1. Nikita Bhangale
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Bhangale, N., Kachhia, K.B. & Gómez-Aguilar, J.F. A new iterative method with \(\rho \)-Laplace transform for solving fractional differential equations with Caputo generalized fractional derivative. Engineering with Computers 38, 2125–2138 (2022). https://doi.org/10.1007/s00366-020-01202-9

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