Best approximations of the ϕ-Hadamard fractional Volterra integro-differential equation by matrix valued fuzzy control functions

Abstract

Abstract In this article, first, we present an example of fuzzy normed space by means of the Mittag-Leffler function. Next, we extend the concept of fuzzy normed space to matrix valued fuzzy normed space and also we introduce a class of matrix valued fuzzy control functions to stabilize a nonlinear ϕ-Hadamard fractional Volterra integro-differential equation. In this sense, we investigate the Ulam–Hyers–Rassias stability for this kind of fractional equations in matrix valued fuzzy Banach space. Finally, as an application, we investigate the Ulam–Hyers–Rassias stability using matrix valued fuzzy control function obtained through the Mittag-Leffler function.

Keywords

• ϕ-Hadamard fractional equation
• Volterra integro-differential equation
• MVFB-space
• Ulam–Hyers–Rassias stability
• Fixed point method