Existence of solutions for fractional differential equations with infinite point boundary conditions at resonance

Abstract

In this paper, by using Mawhin's continuation theorem, we establish some sufficient conditions for the existence of at least one solution for a class of fractional infinite point boundary value problem at resonance. Moreover, an example is given to illustrate our results. MSC: 34A08; 34B15

On solutions of nonlinear BVPs with general boundary conditions by using a generalized Riesz–Caputo operator

“…We present basic perspectives on the existence and uniqueness of solutions of fractional differential equations. Motivated by [30,31], we provide the analysis on existence of solutions for the following nonlinear fractional differential equation involving generalized Riesz-Caputo type derivative operator with general boundary conditions:…”

Existence Results for an m-Point Mixed Fractional-Order Problem at Resonance on the Half-Line

“…When the corresponding homogeneous equation of a fractional boundary value problem (FBVP) has a trivial solution then the FBVP is a non-resonance problem and its solution can be obtained using fixed point theorems, see [4][5][6][7] and the references cited therein. When the homogeneous equation of a FBVP has a non-trivial solution then the problem is a resonance problem and the solution can be obtained using topological degree methods [8][9][10][11][12][13][14][15].…”

Existence of multiple positive solutions for a class of infinite-point singular p-Laplacian fractional differential equation with singular source terms

“…According to introducing height functions, the author obtained the existence and multiplicity of positive solution theorems, and Zhang and Zhai obtained the existence and uniqueness of positive solution for this equation in [18]. In [19], Zhang and Liu investigated the following infinite-point fractional differential equation:…”

“…Motivated by the excellent results above, in this paper, the existence of multiple positive solutions are obtained for a singular infinite-point p-Laplacian boundary value problems. Compared with [19], the equation in this paper is p-Laplacian fractional differential equation, and the method which we used in this paper is Avery-Peterson fixed point theorem. Compared with [12], fractional derivative is involved in the nonlinear terms for BVP (1), (2), and multiple positive solutions are obtained for the BVP (1), (2).…”