Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations

• Published in: Mathematical methods in the applied sciences Vol. 43; no. 15; pp. 8608 - 8631
• Main Authors: Mali, Ashwini D., Kucche, Kishor D.
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 01.10.2020
• Subjects: Boundary conditions; Boundary value problems; Derivatives; Differential equations; Equivalence; existence of solution; implicit nonlinear fractional differential equations; Integral equations; Integrals; Mathematical analysis; Nonlinear equations; nonlocal integral boundary conditions; Ulam‐Hyers stability; Ψ‐Hilfer fractional derivative
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.6521

In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving Ψ‐Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam–Hyers, and Ulam–Hyers–Rassias stability have been acquired by means of an equivalent fractional integral equation. Our investigations depend on the fixed‐point theorem due to Krasnoselskii and the Gronwall inequality involving Ψ‐Riemann–Liouville fractional integral. Finally, examples are provided to show the utilization of primary outcomes.