Existence, Uniqueness and the Multi-Stability Results for a W-Hilfer Fractional Differential Equation

Abstract

In this paper, we apply the well-known aggregation mappings on Mittag-Leffler-type functions to investigating new approximation error estimates of a W-Hilfer fractional differential equation, by a different concept of Ulam-type stability in both bounded and unbounded domains.

Hyers-Ulam stability and continuous dependence of the solution of a nonlocal stochastic-integral problem of an arbitrary (fractional) orders stochastic differential equation

“…Over the years, fractional differential equations and its applications have gotten extensive attention, it is widely used in various disciplines, interested researchers can see the work in [4,9,12,17,31,34]. Many authors have been interested to study fractional stochastic differential equations (see [1,2,5,8,10,11,13,15,19,21,27,28]). The existence and uniqueness of solutions to stochastic differential equations have been studied by many authors see [14,16,18,25].…”