Best approximation of a nonlinear fractional Volterra integro-differential equation in matrix MB-space

Abstract

Abstract In this article, we introduce a class of stochastic matrix control functions to stabilize a nonlinear fractional Volterra integro-differential equation with Ψ-Hilfer fractional derivative. Next, using the fixed-point method, we study the Ulam–Hyers and Ulam–Hyers–Rassias stability of the nonlinear fractional Volterra integro-differential equation in matrix MB-space.

Keywords

• Hyers–Ulam stability
• Fractional Volterra integral
• Ψ-Hilfer fractional derivative
• Integro-differential equations
• Matrix MB-space