Darboux problem for proportional partial fractional differential equations

Abdellatif Ben Makhlouf, Mondher Benjemaa, Djalal Boucenna and Mohamed Ali Hammami

Chaos, Solitons & Fractals, 2023, vol. 166, issue C

Abstract: In this paper, we introduce and study a novel fractional derivative called the generalized proportional Caputo fractional derivative. Under adequate assumptions on the source term, we prove existence and uniqueness aspects of the Darboux problems involving the generalized proportional fractional operator. A numerical scheme based on finite differences approximation is also investigated, and results of convergence are established. Several numerical tests are performed in illustration.

Keywords: Generalized proportional Caputo fractional derivative (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010852

DOI: 10.1016/j.chaos.2022.112906

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