A Survey on Existence Results for Boundary Value Problems of Hilfer Fractional Differential Equations and Inclusions

Abstract

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.

An Existence Result for ψ-Hilfer Fractional Integro-Differential Hybrid Three-Point Boundary Value Problems

“…Substituting the constants c 1 and c 2 into (18), we obtain the integral equation in (15) as desired.…”

“…Numerous monographs have appeared devoted to fractional differential equations, for example, see [1][2][3][4][5][6][7][8]. Recently, differential equations and inclusions equipped with various boundary conditions have been widely investigated by many researchers (see [9][10][11][12][13][14][15][16][17][18] and the references cited therein).…”

A Note on a Coupled System of Hilfer Fractional Differential Inclusions

“…Recently, many papers in the literature have been devoted to the study of fractional differential equations and inclusions defined by the Hilfer fractional derivative (e.g., [8][9][10][11] etc.). We point out that a complete survey on this field of study may be found in [8].…”

“…Recently, many papers in the literature have been devoted to the study of fractional differential equations and inclusions defined by the Hilfer fractional derivative (e.g., [8][9][10][11] etc.). We point out that a complete survey on this field of study may be found in [8]. Taking into account this new trend in research, our intention is to contribute to the development of this topic by establishing new results for a particular class of problems.…”

Analytical Approaches on the Attractivity of Solutions for Multiterm Fractional Functional Evolution Equations

“…The greater part of the current work is concentrated on the existence and uniqueness of the solution for FEE (see [14][15][16]). The goal of this study is to investigate the existence of solutions to a class of multiterm FFEE on an unbounded interval in terms of bounded and consistent capacities.…”