Positive Solutions for a System of Fractional Integral Boundary Value Problems Involving Hadamard‐Type Fractional Derivatives

Abstract

In this paper, we use fixed-point index to study the existence of positive solutions for a system of Hadamard fractional integral boundary value problems involving nonnegative nonlinearities. By virtue of integral-type Jensen inequalities, some appropriate concave and convex functions are used to depict the coupling behaviors for our nonlinearities fii=1, 2.

Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems

“…where α ∈ (1, 2] and b, η, f satisfy (H1)-(H2). Using a similar argument as in Lemmas 2 and 3 of [24], we obtain the following result.…”

“…Research on Hadamard fractional differential equations is at an early stage; see for example [19][20][21][22][23][24][25][26][27][28][29][30]. In [19], B. Ahmad and S. K. Ntouyas used fixed point theory to study the existence and uniqueness of solutions for a Hadamard type fractional differential equation involving integral boundary conditions…”

Existence and Nonexistence of Positive Solutions for High-Order Fractional Differential Equation Boundary Value Problems at Resonance

“…which implies that FBVP (1) happens to be at resonance. By virtue of the widespread applications, various differential equations have been studied by many researchers (see [1][2][3][4][5][6][7][8][9][10][11][12][13] and the references therein). Fractional-order models can describe many processes more accurately than integer-order models, and a great deal of papers focusing on FBVPs appeared in recent years (see [14][15][16][17][18][19][20][21][22][23]).…”

Three-Order Multipoint Boundary Value Problems for p-Laplacian Operator on Time Scales

“…Recently, for the existence of positive solutions of multipoint boundary value problems, some authors have obtained the existence results. The differential equations offer wonderful tools for describing various natural phenomena arising from natural sciences and engineering, many numerical and analytical results, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, the multipoint boundary value problems treated in the above mentioned references do not discuss the problems with singularities and the there-order p-Laplacian operator.…”