Solutions for Integral Boundary Value Problems of Nonlinear Hadamard Fractional Differential Equations

Abstract

In this paper using fixed point methods we establish some existence theorems of positive (nontrivial) solutions for integral boundary value problems of nonlinear Hadamard fractional differential equations.

Nontrivial Solutions for a Higher Order Nonlinear Fractional Boundary Value Problem Involving Riemann-Liouville Fractional Derivatives

“…Conditions similar to (H1) Wang and (H2) Wang can be found in [2][3][4][5][6][7][8][9]. In [2], the authors studied the existence of positive solutions for the nonlinear fractional differential equation:…”

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

“…Hadamard fractional-order problems were briefly discussed in the literature; see [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72] and the references therein. Yang in [53] used the comparison principle and the monotone iterative technique combined with the subsolution and supersolution method to study the existence of extremal solutions for Hadamard fractional differential equations with Cauchy initial value conditions…”

“…where D α a+ , J α a+ are the left-sided Hadamard fractional derivative and integral of order α, respectively. In [54], the authors used fixed point methods to study the existence of positive solutions for Hadamard fractional integral boundary value problems…”

Solvability for a class of nonlinear Hadamard fractional differential equations with parameters

“…Although many researchers are paying more and more attention to Hadamard type fractional differential equation, the study of the topic is still in its primary stage. For details and recent developments on Hadamard fractional differential equations, see [41][42][43][44][45][46][47][48].…”