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

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.

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. We set…”

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

“…and get the best approximation with a better estimate for the pseudo ψ-Hilfer fractional Volterra integral equation. Our method can be used for new problems; for more problems and details, we refer to [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. 4)- (7).…”