A note on the existence of Hilfer fractional differential inclusions with almost sectorial operators

Abstract

In this paper, we mainly focus on the existence of the mild solution for the Hilfer fractional differential inclusions with almost sectorial operators. By using the results on the fractional calculus, sectorial operators, semigroup theory, and Dhage's fixed point theorem, we prove the primary results. Finally, an example is presented to demonstrate the theory obtained.

Approximate controllability of Ψ‐Caputo fractional differential equation

“…Numerous studies have been done to determine whether there are solutions for fractional differential systems and whether there are solutions for fractional differential inclusions. To validate the discussion of theory and its application connected to fractional calculus, the given research papers [1][2][3][4][5][6][7][8][9][10][11][12] can be consulted.…”

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.…”

Existence of Hilfer Fractional Stochastic Differential Equations with Nonlocal Conditions and Delay via Almost Sectorial Operators

“…Hilfer fractional calculus has been the subject of several academic works, especially [20,[27][28][29]. Researchers found a mild solution for HFD systems using almost sectorial operators and a fixed-point technique, according to [30][31][32][33].…”

“…Researchers have also established a theory that uses fractional calculus, semigroup operators, multivalued maps, the measure of noncompactness, the transfer function, the Wright function, and the fixed-point technique to infer different features of linked semigroups formed by almost sectorial operators. For further information, we can refer to [30,[33][34][35][36][37]. In [30][31][32], researchers used Schauder's fixed-point theorem to arrive at their conclusions via almost sectorial operators.…”