Analysis of a Nonlinear ψ-Hilfer Fractional Integro-Differential Equation Describing Cantilever Beam Model with Nonlinear Boundary Conditions

Abstract

In this paper, we establish sufficient conditions to approve the existence and uniqueness of solutions of a nonlinear implicit ψ-Hilfer fractional boundary value problem of the cantilever beam model with nonlinear boundary conditions. By using Banach’s fixed point theorem, the uniqueness result is proved. Meanwhile, the existence result is obtained by applying the fixed point theorem of Schaefer. Apart from this, we utilize the arguments related to the nonlinear functional analysis technique to analyze a variety of Ulam’s stability of the proposed problem. Finally, three numerical examples are presented to indicate the effectiveness of our results.

Existence and stability results for a sequential $ψ$-Hilfer fractional integro-differential equations with nonlocal boundary conditions

“…In [27], the authors established sufficient conditions to approve the existence and uniqueness of solutions of a nonlinear implicit ψ-Hilfer fractional boundary value problem of the cantilever beam model with nonlinear boundary conditions…”