Radu–Miheţ Method for the Existence, Uniqueness, and Approximation of the ψ-Hilfer Fractional Equations by Matrix-Valued Fuzzy Controllers

Abstract

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate a fractional Volterra integro-differential equation with the ψ-Hilfer fractional derivative in matrix-valued fuzzy k-normed spaces to obtain an approximation for this type of fractional equation.

Existence–Uniqueness and Wright Stability Results of the Riemann–Liouville Fractional Equations by Random Controllers in MB-Spaces

“…In 2008, Mihet and Radu [16,17] introduced a new method to investigate random stability in MB-spaces and then some authors used this method to get stability results for new equations [18][19][20][21][22][23][24][25][26][27][28][29][30]. Here, we use the Mihet and Radu method and Theorem 1 to investigate random Wright stability of (3) and improve recent results [31]; we can suggest [32][33][34] for more details.…”

Minimum Superstability of Stochastic Ternary Antiderivations in Symmetric Matrix-Valued FB-Algebras and Symmetric Matrix-Valued FC-⋄-Algebras

“…We call this set the set of all contraction mappings that is, every contractive function is located in this set. Next, we present the Diaz-Margolis theorem (FTP) [5,6,8,9]. Theorem 1.…”

“…It is easy to see that T M is a complete generalized metric space (CGMS) [5,6,8]. In the following, for all u ∈ M, we define a stochastic linear mapping S : Υ → Υ as follows:…”

“…The study of the stability problem for group homomorphisms started with the famous Ulam question in 1940, and in 1941 Hyers established the stability of nonlinear functions in a particular case.In 1978, Rassias extended this problem and now it is known as the Hyers-Ulam-Rasias problem.Various aspects of the Hyers-Ulam stability for various functions and mappings have been investigated and among these equations and mappings, we refer the reader to Euler-Lagrange functional equations (E-L-FE), differential equations (DE), Navier-Stokes equations (N-SE), as well as mappings such as Cauchy-Jensen mappings, k-additive mappings, multiplicative mappings [1][2][3][4]. Most of the investigations have been carried out in Banach spaces and now research is conducted in other spaces as well [5][6][7][8]. Also, the stability of groups, Banach algebra, ternary Banach algebras, and C-ternary algebras have attracted the attention of many researchers [9][10][11].…”

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

“…In this paper, we consider an MVkFB-space introduced in [10] and consider a modern class of the MVF control function based on the H-Fox functions. Our goal is to obtain an approximation for the conformable fractional diferential equation using the alternative fxed-point theorem in MVkFB-spaces.…”