Positive Solutions for a System of Fractional Differential Equations with Nonlocal Integral Boundary Conditions

Abstract

In this paper, we discuss by means of a fixed point theorem, the existence of positive solutions of a system of nonlinear Caputo fractional differential equations with integral boundary conditions. An example is given to illustrate the main results.

Existence of Triple Positive Solutions to a Four-Point Boundary Value Problem of a Fractional Differential Equations

“…Due to the development of the theory of fractional calculus and its applications, such as Bode􀆳s analysis of feedback amplifiers, aerodynamics and polymer rheology in the fields of physics, etc, many works on the basic theory of fractional calculus and fractional order differential equations have been done [1][2][3][4][5][6][7] . Recently, there have been many papers dealing with the solutions or positive solutions to boundary value problems for nonlinear fractional differential equations (FBVPs) with local boundary conditions [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and nonlocal boundary conditions [24][25][26][27][28][29][30][31][32][33][34][35] and references along this line.…”

Existence, uniqueness, and Hyers–Ulam stability of solutions to nonlinear p‐Laplacian singular delay fractional boundary value problems

“…Lakoud and Ashyralyev 20 investigated positive solutions for a system of fractional differential equations with nonlocal integral boundary conditions. Dhage and Jadhav 21 studied basic results in the theory of hybrid differential equations with linear perturbations of second type.…”

Existence of solutions for a nonlinear fractional system with nonlocal boundary conditions

“…It is to be noted that such theory has many applications in several events existing in the real world, and also in many sciences such as: engineering, physics, chemistry, biology, etc ..., [13]. Moreover, the study of the systems of fractional differential equations has become more and more popular tool for controlling and modeling different systems [2,7,[15][16][17]. Thus the fixed point theory is a powerful mathematical tool in the study of the existence, uniqueness, positivity and stability of solutions, see [1,[3][4][5][6][9][10][11][12][13][14].…”