Existence results for a fractional boundary value problem with fractional Lidstone conditions

Abstract

Our aim in this work is to study the existence of solutions for a fractional Lidstone boundary value problems. We use some fixed point theorems to show the existence and uniqueness of solution under suitable conditions. Two examples are given to ilustrate the obtained results.

Existence and uniqueness of solutions for multi-order fractional differential equations with integral boundary conditions

“…Since fractional-order models are more accurate than integer-order models, fractional differential equations, which have profound physical backgrounds and rich theoretical connotations, have attracted much attention. Recently, many scholars have studied the properties of solutions to some BVPs of fractional differential equations by using Banach contraction mapping principle, Leray-Schauder nonlinear alternative, Guo-Krasnoselskii fixed point theorem, monotone iterative technique, and so on [7][8][9][10][11][12][13][14][15][16].…”

Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions

“…In the past decades, the existence of solutions or positive solutions for boundary value problems (BVPs for short) of nonlinear fractional differential equations attracted considerable attention from many authors, see [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and the references therein.…”

Existence and Uniqueness of Solutions for BVP of Nonlinear Fractional Differential Equation

“…= (0) = ⋅ ⋅ ⋅ = ( −2) (0) = 0, ( 0+ )(1) = 0; see papers [10][11][12][13][14][15][16], respectively. see papers [17,18], respectively.…”