Positive Solutions for a System of Semipositone Fractional Difference Boundary Value Problems

Abstract

Using the fixed point index, we establish two existence theorems for positive solutions to a system of semipositone fractional difference boundary value problems. We adopt nonnegative concave functions and nonnegative matrices to characterize the coupling behavior of our nonlinear terms.

Positive solutions for a class of fractional difference systems with coupled boundary conditions

“…They used the Guo-Krasnosel'skii fixed point theorem to obtain the existence of positive solutions for (1.3), and they also presented intervals for parameters λ and μ for the positive solutions. However, as is mentioned by Christopher S. Goodrich in [28], there has been little work done in fractional difference equations, we only refer to [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. For example, in [29] the authors studied discrete fractional calculus and offered some important properties of the fractional sum and the fractional difference operators.…”

Positive Solutions for a Hadamard Fractional p-Laplacian Three-Point Boundary Value Problem

“…where D α 0+ denotes the Riemann-Liouville fractional derivative. Positive solutions [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and nontrivial solutions [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] were also studied for fractional-order equations. For example, the authors in [16] used the Guo-Krasnoselskii's fixed-point theorem and the Leggett-Williams fixed-point theorem to study the existence and multiplicity of positive solutions for the fractional boundary-value problem…”

Multiplicity Results to a Conformable Fractional Differential Equations Involving Integral Boundary Condition

“…In recent years, fractional differential equations have exerted tremendous influence on some mathematical models of research processes and phenomena in many fields such as electrochemistry, heat conduction, underground water flow, and porous media. A growing number of papers deal with the existence or multiplicity of solutions of initial value problem and boundary value problem for fractional differential equations [1][2][3][4][5][6][7][8][9][10][11]. Recently, the authors [12] give an interesting fractional derivative called the "conformal fractional derivative", which depends on the limit definition of the function derivative.…”