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arXiv · 2001.08479

Nonlocal Boundary Value Problem for Generalized Hilfer Implicit Fractional Differential Equations

Ashwini D. Mali·Kishor D. Kucche
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Abstract

In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving $φ$-Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam-Hyers, and Ulam-Hyers-Rassias stability has been acquired by means equivalent fractional integral equation. Our investigations depend on the fixed point theorem due to Krasnoselskii and the Gronwall inequality involving $φ$-Riemann--Liouville fractional integral. An example is provided to show the utilization of primary outcomes.

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Ashwini D. Mali, Kishor D. Kucche. 2020-01-23. Nonlocal Boundary Value Problem for Generalized Hilfer Implicit Fractional Differential Equations. https://doi.org/10.1002/mma.6521

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