Hilfer Fractional Neutral Stochastic Volterra Integro-Differential Inclusions via Almost Sectorial Operators

Abstract

In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the result. In addition, an illustration of the principle is provided.

Existence of Mild Solutions for Nonlocal Evolution Equations with the Hilfer Derivatives

“…The existence of mild solutions for a Hilfer fractional evolution system is investigated in [29]. Sivasankar and Udhayakumar [30] investigated the existence of neutral stochastic Volterra integrodifferential inclusions with the Hilfer derivative and with almost sectorial operators. Basic fractional calculus theory, Bohnenblust-Karlin's fixed point theorem, and stochastic analysis were utilized.…”

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).…”

“…Ahmed and Borai [27] created the HF stochastic integro-differential equations. Very recently, researchers [21,28,29] explored HF integro-differential systems with almost sectorial operators by applying the fixed point approach. But as far as we are aware, no study on HF neutral stochastic integro-differential evolution HVIs with OC has been documented in the literature.…”

Existence of Mild Solutions for Hilfer Fractional Neutral Integro-Differential Inclusions via Almost Sectorial Operators

“…is the R − L integral of order 1 − q, A is an almost sectorial operator on a complex Banach space. We refer the reader to [34][35][36][37] for information. These discoveries led us to extend past findings in the literature to Hilfer fractional Volterra-Fredholm integro-differential inclusions.…”