Existence of a Unique Solution and the Hyers–Ulam‐H‐Fox Stability of the Conformable Fractional Differential Equation by Matrix‐Valued Fuzzy Controllers

Abstract

In this paper, we consider a conformable fractional differential equation with a constant coefficient and obtain an approximation for this equation using the Radu–Mihet method, which is derived from the alternative fixed- point theorem. Considering the matrix-valued fuzzy k-normed spaces and matrix-valued fuzzy H-Fox function as a control function, we investigate the existence of a unique solution and Hyers–Ulam-H-Fox stability for this equation. Finally, by providing numerical examples, we show the application of the obtained results.

Existence, uniqueness, and averaging principle for Hadamard Itô–Doob stochastic delay fractional integral equations

“…The autodidact Oliver Heaviside introduced the practical use of fractional differential operators in the analysis of an electrical transmission around 1890. The theory and applications of fractional calculus developed considerably during the 19th and 20th centuries, and many contributors gave definitions for fractional derivatives and integrals (see previous works [1][2][3][4][5][6][7]). Indeed, the authors in Kumaret al [6] have studied the existence and uniqueness for generalized Caputo-type initial value problems with delay.…”

Caputo-hadamard Fractional Differential Equations: Integral Boundary Condition System

“…By utilizing various fixed point methodologies, several researchers have concentrated on some intriguing findings regarding the existence of solutions to the fractional differential equation with beginning and boundary conditions (see [1,14,26,29,30,31,32,37]). Today, The fractional differential equations with Hadamard derivative is quickly increasing with the support of numerous research of fixed point theory, topology, and non-linear analysis ( see [11,9,23,39,46,18]).…”