Abstract
In this research, we present the stability analysis of a fractional differential equation of a generalized Liouville–Caputo-type (Katugampola) via the Hilfer fractional derivative with a nonlocal integral boundary condition. Besides, we derive the relation between the proposed problem and the Volterra integral equation. Using the concepts of Banach and Krasnoselskii’s fixed point theorems, we investigate the existence and uniqueness of solutions to the proposed problem. Finally, we present two examples to clarify the abstract result.
Highlights
Fractional calculus is a branch of mathematics that examines the properties of derivatives and integrals of arbitrary non-integer order
6 Conclusions In this article, we have shown that the proposed problem (1.6) is equivalent to the Volterra integral equation
Riemann–Liouville integral condition reduces to the one considered in [20, 44, 48, 49]
Summary
Fractional calculus is a branch of mathematics that examines the properties of derivatives and integrals of arbitrary non-integer order. Many researchers studied the existence and uniqueness of solutions for boundary value problems (BVPs) of fractional differential equations with different types of fractional integrals and derivatives; see for example [5, 7, 13, 17, 25, 33, 36, 40,41,42,43, 45, 52, 55]. Suphawat et al [12] initiated research and found existence and uniqueness results for the boundary value problems (BVPs) which involve Hilfer fractional derivatives and a nonlocal. We show the equivalence between problem (1.6) and the Volterra integral equation and apply the Banach and Krasnoselskii’s fixed point theorems to establish the existence and uniqueness results.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
