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Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative

    Mohammed S. Abdo Affiliation
    ; Satish K. Panchal Affiliation
    ; Hussien Shafei Hussien Affiliation

Abstract


Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam-Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii's fixed point theorem. An example is provided to illustrate our main results.

Keyword : fractional integro-differential equations, ψ -Hilfer fractional derivative, ψ-fractional integral, existence and and Ulam-Hyers stability, fixed point theorem, Mittag-Leffler function, least squares method

How to Cite
Abdo, M. S., Panchal, S. K., & Shafei Hussien, H. (2019). Fractional integro-differential equations with nonlocal conditions and ψ–Hilfer fractional derivative. Mathematical Modelling and Analysis, 24(4), 564-584. https://doi.org/10.3846/mma.2019.034
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Oct 25, 2019
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