Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

Abstract

In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.

On the nonlinear Hadamard-type integro-differential equation

“…In 2018, Matar [ 20 ] obtained the solution of the linear equations with the initial conditions (three terms on the left-hand side at most and a given function on the right) by the parameter technique, and then investigated the existence problems of the corresponding nonlinear types of Hadamard equations using fixed point theorems. Very recently, Ding et al [ 21 ] applied the fixed point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities. In 1967, Caputo [ 22 ] introduced another type of fractional derivative which has an advantage over R-L derivative in differential equations since it does not require to define fractional order initial conditions.…”

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

“…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…”

Positive Solutions for a Weakly Singular Hadamard-Type Fractional Differential Equation with Changing-Sign Nonlinearity

“…In particular, the Hadamard derivative is a nonlocal fractional derivative with singular logarithmic kernel. So the study of Hadamard fractional differential equations is relatively difficult; see [26][27][28][29][30][31][32].…”