Optimal control results for impulsive fractional delay integrodifferential equations of order 1 < r < 2 via sectorial operator

Abstract

This research investigates the existence of nonlocal impulsive fractional integrodifferential equations of order 1 &lt; r &lt; 2 with infinite delay. To begin with, we discuss the existence of a mild solution for the fractional derivatives by using the sectorial operators, the nonlinear alternative of the Leray–Schauder fixed point theorem, mixed Volterra–Fredholm integrodifferential types, and impulsive systems. Furthermore, we develop the optimal control results for the given system. The application of our findings is demonstrated with the help of an example.

An analysis on the approximate controllability outcomes for fractional stochastic Sobolev‐type hemivariational inequalities of order 1 < r < 2 using sectorial operators

“…Very recently, Mohan Raja et al [28, 47, 48] have developed the existence, optimal controls, and approximate controllability results for fractional derivatives of order $$$ r\in \left(1,2\right) $$$ by utilizing the sectorial operators, integrodifferential systems, multivalued functions, and various fixed‐point techniques. Johnson et al [24, 49] discussed the effectiveness of optimal controllability in fractional order $$$ r\in \left(1,2\right) $$$ by utilizing sectorial operators, stochastic systems, impulsive conditions, and fixed‐point approaches. However, these results only pay attention to the controllability results for a class of fractional system of order $$$ r\in \left(1,2\right) $$$ via sectorial operator without stochastic hemivaritional inequality, which is the main motivation to consider no work has been reported in the literature about the approximate controllability of fractional stochastic Sobolev‐type hemivariational inequalities of order $$$ r\in \left(1,2\right) $$$ on sectorial operator.…”

An analysis concerning to the existence of mild solution for Hilfer fractional neutral evolution system on infinite interval

“…Differential equations with fractional derivatives can describe various phenomena, including viscoelasticity, electrochemistry, and nonlinear oscillation in mechanics. For more information, reference the basic books [1–7] and the relevant research articles [8–14]. Very recently, many authors have developed existence results for a coupled system of fractional‐order hybrid boundary value problems with $$$ n $$$ initial and boundary hybrid conditions by using the Hyers–Ulam stability criteria, the measure of noncompactness, degree theory, the Atangana–Baleanu fractional derivative, the $$$ p $$$‐Laplacian operator, and the typhoid model in previous studies [15–18].…”

A second order numerical method for singularly perturbed Volterra integro-differential equations with delay

“…The existence and unique solution of functional integro-differential equation with nonlocal condition and finite delay function has been investigated in [8]. In [9], the existence of nonlocal impulsive fractional integro-differential equations of order 1 < r < 2 with infinite delay has been investigated. Approximate controllability of a second-order Volterra-Fredholm stochastic differential integral system including delay and impulses is investigated by Ma et al [10].…”