Existence and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators

Abstract

In this article, we are concerned with the existence of mild solutions and approximate controllability of Hilfer fractional evolution equations with almost sectorial operators and nonlocal conditions. The existence results are obtained by first defining Green’s function and approximate controllability by specifying a suitable control function. These results are established with the help of Schauder’s fixed point theorem and theory of almost sectorial operators in a Banach space. An example is also presented for the demonstration of obtained results.

Finite-Approximate Controllability of Riemann–Liouville Fractional Evolution Systems via Resolvent-Like Operators

“…Then, (T − t) α−1 ∑ ∞ n=1 E α,α −λ n (T − t) α (g, e n )e n (θ) = 0 on ω × (0, T). By Proposition 4.2 [58], g = 0 on Ω × (0, T), which is equivalent to the linear system associated with Equation (29). Thus, the system (29) is finite-approximately controllable on [0, T], provided that the nonlinear term f is bounded.…”

“…Bedi [29], Matar [30], Ge et al [31], Grudzka and Rykaczewski [32], Ke et al [33], Kumar and Sukavanam [34,35], Liu and Li [36], Sakthivel et al [37], Wang et al [38], Yan [39], Yang and Wang [40], Rykaczewski [41], Mahmudov and McKibben [42,43], Ndambomve and Ezzinbi [44] have used different methods to study approximate controllability for several fractional differential and integro-differential systems.…”

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

“…Hilfer fractional calculus [6,[8][9][10][11]13] has been the subject of several articles. Researchers revealed the existence of the mild solution for Hilfer fractional differential systems via almost sectorial operators using a fixed point approach in [4,15,16]. The authors investigated the solvability and controllability of differential systems using a fixed point technique in [17,27].…”

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

“…Other fractional derivatives introduced by Hilfer [22] include the R-L derivative and Caputo fractional derivative. Many scholars have recently shown tremendous interest in this area, e.g., [23][24][25]; researchers have established their results with the help of Schauder's fixed point theorem. In [26][27][28], the authors worked on the existence and controllability of differential inclusions via the fixed point theorem approach.…”