Ulam–Hyers–Rassias stability for nonlinear Ψ-Hilfer stochastic fractional differential equation with uncertainty

Abstract

We consider a nonlinear Cauchy problem involving the Ψ-Hilfer stochastic fractional derivative with uncertainty, and we give a stability result. Using fixed point theory, we are able to provide a fuzzy Ulam–Hyers–Rassias stability for the considered nonlinear stochastic fractional differential equations.

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

“…Our results can be applied to improve recent results [5], and by the methods used in this paper, we can extend some fractional Volterra integro-differential equations in MVF-k-Bspaces [11][12][13][14].…”

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.…”

The stability of the fractional Volterra integro‐differential equation by means of Ψ‐Hilfer operator revisited

“…On the other hand, the fractional calculus since its first ideas, and consequently its consolidation in several areas of knowledge, allowed and has belonged and providing results of great impact in the scientific community, in particular, involving applications in biology, medicine, engineering, among others 10–12 and references therein. We want to highlight the fundamental role of the theory of fractional differential equations, since it has been the target of investigation and has been growing during these last decades, in particular, in the investigation of Ulam‐Hyers stabilities, existence, and uniqueness 13–22 …”

“…After the introduction of the fractional derivative ψ ‐Hilfer, 23 which owns a wide class of fractional derivatives, researchers around the world started several researches involving such operator, in particular, on the Ulam‐Hyers stability 13,14,18,24 and references therein.…”