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Analysis and numerical solution of the generalized proportional fractional Cauchy problem
Applied Numerical Mathematics • 2021
Publication Information
Authors
D. Boucenna; D. Baleanu; Abdellatif Ben Makhlouf; A. M. Nagy
Keywords
Fractional differential equations; Generalized proportional fractional derivative
Journal
Applied Numerical Mathematics
Publisher
Elsevier
Volume
167
Issue
Not Available
Pages
173-186
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
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.