J. Nonl. Evol. Equ. Appl. 2023 (1), pp. 1-18, published on May 24, 2023:

Fractional Pantograph Differential Equations with Periodic Conditions via Ψ−Caputo Derivative

Soufyane Bouriah(a), Djamal Foukrach(a), Mouffak Benchohra(b) and Gaston N’Guérékata(c),

(a) Department of Mathematics, Faculty of Exact Sciences and Informatics, University Hassiba Benbouali of Chlef, Algeria
(b) Laboratory of Mathematics, University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
(c) Department of Mathematics, NEERLab, Morgan State University, 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA

Received on September 11, 2022, revised on January 7 and February 5, 2023.
Accepted on February 5, 2023

Communicated by Gisèle Mophou-Loudjom

Abstract.  In this paper, we present the existence and uniqueness criteria of the solutions for a wide class of nonlinear fractional pantograph differential equations involving Ψ−Caputo fractional derivative supplemented with periodic conditions. The main tools of our study include the Mawhin’s coincidence theory. An example is constructed to illustrate the application of the obtained findings.
Keywords: Coincidence degree theory, existence, uniqueness, Ψ-Caputo fractional derivative.
2010 Mathematics Subject Classification:   34A08, 34B10, 34B40.

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