Stability of the fractional Volterra integro‐differential equation by means of ψ‐Hilfer operator

By J. Sousa, F. G. Rodrigues, E. Capelas de Oliveira. Mathematical methods in the applied sciences, 2018

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In this paper, using the Riemann‐Liouville fractional integral with respect to another function and the ψ−Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro‐differential equation. In this sense, for this new fractional Volterra integro‐differential equation, we study the Ulam‐Hyers stability and, also, the fractional Volterra integral equation in the Banach space, by means of the Banach fixed‐point theorem. As an application, we present the Ulam‐Hyers stability using the α‐resolvent operator in the Sobolev space W1,1(R+,C) .

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/2ab207a208463325c01e0f4f7a1999f6a7d9eeee

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Ulam–Hyers–Rassias Stability for a Class of Fractional Integro-Differential Equations (2018, methodology): “Recently, using the ψ-Hilfer fractional derivative and the Banach fixed-point theorem, a considerable attention was paid to the study of the stability of Ulam-Hyers and Ulam-Hyers-Rassias involving a nonlinear differential integral equation [30, 31, 32].”
On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation (2018, background): “In this sense, there are already some works on existence, uniqueness and stability of the Ulam-Hyers type involving the ψ-Hilfer fractional derivative, since it is a global and very general differential operator [15, 28, 29, 30, 31, 32].”