Solutions for a category of singular nonlinear fractional differential equations subject to integral boundary conditions

Abstract

We concentrate on a category of singular boundary value problems of fractional differential equations with integral boundary conditions, in which the nonlinear function f is singular at $t=0$ t = 0 , 1. We use Banach’s fixed-point theorem and Hölder’s inequality to verify the existence and uniqueness of a solution. Moreover, also we prove the existence of solutions by Krasnoselskii’s and Schaefer’s fixed point theorems.

Solvability of a Hadamard Fractional Boundary Value Problem at Resonance on Infinite Domain

“…In recent decades, due to the broad application of fractional calculus in many fields, such as chemical physics, electrical networks, signal and image processing, modeling for anomalous diffusion, and fluid flow, there has been significant development in both the theory and applications of fractional calculus [1][2][3][4][5][6]. There exist many types of fractional derivatives, such as Riemann-Liouville, Caputo, Hadamard, Grunwald-Letnikov, and Weyl.…”

Existence Results of a Singular Non-linear Fractional Differential Equations Class with Nonlocal Double Integral Boundary Conditions

“…Researchers are also interested in singular nonlinear FDEs with integral boundary conditions [36][37][38][39][40]. Yan [40] investigated just such a problem.…”

“…Researchers are also interested in singular nonlinear FDEs with integral boundary conditions [36][37][38][39][40]. Yan [40] investigated just such a problem. Specifically, the upcoming problem was studied Subject to conditions: 𝑥(0) = 0 = 𝑥(0) ′ and…”