Positive solutions for nonlinear Hadamard fractional differential equations with integral boundary conditions

Abstract

ABSTRACT:We investigate the existence of positive solutions for a class of nonlinear Hadamard fractional differential equations with integral boundary conditions. By using the properties of Green's functions and the KrasnoselskiiZabreiko fixed point theorem, two new existence results for at least one positive solution are obtained. Two examples are given to illustrate the main results.

Existence, uniqueness, and multiplicity results on positive solutions for a class of Hadamard‐type fractional boundary value problem on an infinite interval

“…Similarly, Yang and Qin employed the Krasnoselskii‐Zabreiko fixed point theorem to investigate the existence of positive solutions of nonlinear Hadamard fractional differential equations with integral boundary conditions: where is the Hadamard‐type fractional derivative of order q , .…”

“…Several research papers dealing with Hadamard-type fractional differential equations with various boundary conditions have been recently published. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] Refer to Ahmad et al 9 for a comprehensive monograph on Hadamard-type fractional differential equations, inclusions, and inequalities.…”

The Unique Positive Solution for Singular Hadamard Fractional Boundary Value Problems

“…An important characteristic of Hadamard fractional derivative is that it contains logarithmic function of arbitrary exponent. However, there are few results about this topic (see [23][24][25][26][27][28]).…”

Eigenvalue problems for nonlinear conformable fractional differential equations with multi-point boundary conditions

“…4-6 and the references quoted therein. By using the properties of Green's functions and the Krasnoselskii-Zabreiko fixed point theorem, Yang and Qin 7 investigated the existence of positive solutions for a class of nonlinear Hadamard fractional differential equations with integral boundary conditions. Zhou 8,9 established sufficient conditions for the existence of globally attractive solutions for the Cauchy problems of fractional differential (evolution) equations in abstract space and in the cases that the semigroup is compact as well as non-compact, respectively.…”