Existence of positive solutions for Riemann–Liouville fractional order three-point boundary value problem

Abstract

In this paper, we study the following fractional order three-point boundary value problem [Formula: see text] where [Formula: see text], are the standard Riemann–Liouville fractional order derivatives with [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]: [Formula: see text] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.

On a coupled system of fractional differential equations with nonlocal non-separated boundary conditions

“…where c D α denotes the Caputo fractional derivative of order α, f is a continuous function on [0, T] × R and a i , b i , c i , i = 1, 2 are real constants such that a 1 + b 1 = 0 and b 2 = 0. The system of fractional differential equations boundary value problems has also received much attention and its research has developed very rapidly; see [2,4,5,8,10,12,13,20,21,25,[31][32][33]35]. Recently, Alsulalt et al [13] established the existence and uniqueness results for a nonlinear coupled system of Caputo type fractional differential equations supplemented with non-separated coupled boundary conditions.…”

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

“…In fact, the fractional differential equations have attracted more and more attention for their useful applications in various fields, such as economics, science, and engineering; see [1][2][3][4][5]. In the last few decades, much attention has been focused on the study of the existence of positive solutions for boundary value problems of Riemann-Liouville type or Caputo type fractional differential equations; see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Multiplicity of positive solutions for coupled system of fractional differential equation with p-Laplacian two-point BVPs

“…Later, these results are further extended to fractional order boundary value problems Ahmad and Nieto [2], Anderson and Avery [3], Bai and Sun [7], Goodrich [8], Rao [13], and Su [18] by applying various fixed point theorems on cones. Recently,researchers are concentrating on the theory of fractional order boundary value problems associated with p-Laplacian operator Lu [11] and Prasad and Krushna [16].…”