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

• Main Authors: Mohammed S. Abdo, Satish K. Panchal, Hussien Shafei Hussien
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2019-10-01
• Series: Mathematical Modelling and Analysis
• Subjects: fractional integro-differential equations; ψ -Hilfer fractional derivative; ψ-fractional integral; existence and and Ulam-Hyers stability; fixed point theorem; Mittag-Leffler function
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/6330
• ISSN: 1392-6292; 1648-3510

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.