New Outcomes Regarding the Existence of Hilfer Fractional Stochastic Differential Systems via Almost Sectorial Operators

Abstract

In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory, sectorial operators, and the fixed-point technique. We start by confirming the existence of the mild solution by using Dhage’s fixed-point theorem. Finally, an example is provided to demonstrate the considered Hilferr fractional stochastic differential systems theory.

A new conversation on the existence of Hilfer fractional stochastic Volterra–Fredholm integro-differential inclusions via almost sectorial operators

“…Furthermore, in [5,6], researchers studied fractional differential inclusion papers using Bohnenblust-Karlin's fixed point theorem for multivalued maps. Sivasankar and Udhayakumar [25] recently used the fixed point approach to investigate the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. However, to the best of our knowledge, so far, no work has been reported in the literature about the existence of Hilfer fractional stochastic Volterra-Fredholm integro-differential inclusions via almost sectorial operators.…”

Approximate Controllability Outcomes of Impulsive Second-Order Stochastic Neutral Differential Evolution Systems

“…Due to their wide variety of applications in describing a spectrum of complex applied mathematics in the scientific, pharmaceutical, and healthcare sectors, stochastic differential systems have piqued interest. One can verify [28][29][30][31][32]. Many physical processes, including fluid flow, aerodynamics, and others, are represented computationally by differential equations; for further information, see [13,[33][34][35].…”

Hilfer fractional neutral stochastic integro‐differential evolution hemivariational inequalities and optimal controls

“…Furthermore, it should be recognised that stochastic pain or noise appears in both natural and artificial systems. Due to its many applications in the biological, physical, and pharmacological sciences (see [20][21][22]), stochastic differential systems have attracted a lot of attention. The authors [23,24] studied the existence of mild solutions of SEEs and their OC in Hilbert spaces (HSs).…”