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Analysis and numerical solution of the generalized proportional fractional Cauchy problem
Journal article   Peer reviewed

Analysis and numerical solution of the generalized proportional fractional Cauchy problem

Djalal Boucenna, D. Baleanu, Abdellatif Ben Makhlouf and A.M. Nagy
Applied numerical mathematics, Vol.167, pp.173-186
09/2021
DOI: https://doi.org/10.1016/j.apnum.2021.04.015

Abstract

Fractional differential equations Generalized proportional fractional derivative
In this paper, we explore the existence and uniqueness theorem for a problem of the fractional Cauchy form, with dependence on the generalized proportional Caputo derivative. Furthermore, a new numerical technique is presented based on a decomposition formula for the generalized proportional Caputo derivative. Convergence analysis of the proposed technique is proved. Finally, numerical results are obtained to confirm the validity of the proposed method.

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