ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

$\psi$-Hilfer Fractional Functional Differential Equation by Picard Operator Method

Journal of Applied Nonlinear Dynamics 9(4) (2020) 685--702 | DOI:10.5890/JAND.2020.12.011

Mohammed A. Almalahi , Mohammed S. Abdo, Satish K. Panchal

Abstract

We present in this article the existence and uniqueness results for a fractional functional differential equation with boundary condition and finite delay involving $\psi-$ Hilfer --type fractional derivative. Next, we establish the equivalent mixed-type integral for boundary condition. Further, the Ulam-Hyers-Mittag-Leffler stability is discussed. The Picard operator method, Banach fixed point theorem, and generalized Gronwall's inequality plays an important role to prove our results. At the end, an illustrative example will be introduce to justify our results.

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