On fractional integro-differential inclusions with state-dependent delay in Banach spaces

Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators

“…Specifically, sufficient conditions for the existence are given by means of the nonlinear alternative of Leray-Schauder type for multivalued maps due to O'Regan with the analytic α-resolvent operator. The known results appeared in [2,7] are generalized to the fractional stochastic multi-valued settings and the case of infinite delay.…”

“…Recently, the analysis of fractional differential equations or inclusions with state-dependent delay has received much attention [2]. Very recently, the existence of solutions to fractional differential inclusions with state dependent delay has been established (see [7] and the references therein). The deterministic models often fluctuate due to noise, which is random or at least appears to be so.…”

“…Sufficient conditions for the existence of solutions are derived by the authors using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O'Regan. Motivated by the previously mentioned works [7,11,23,25], in this paper, we consider the existence of a class of fractional partial neutral stochastic integro-differential inclusions with state-dependent delay of the form…”

Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay

“…Along these lines, all models viewed regarding FDE that may be existence of solutions, continuous dependence and parameters are also available in the concept of FDI-considering the fact that FDI occur in the mathematical modelling of specific models in financial aspects, optimal control, etc. and are usually investigated by numerous writers (see, for instance, [22][23][24] and the references therein). Fractional equation with delay properties arise in several fields such as biological and physical with state-dependent delay (SDD) or non-constant delay.…”

“…Nowadays, existence results of mild solutions for such problems became very attractive and several researchers are working on it. Recently, several papers have been written on the fractional order problems with SDD [23,[25][26][27][28][29][30][31][32][33][34][35][36] and the sources therein.…”