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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

Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad-431004, (M.S.), India

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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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