Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions

Positive solutions for a system of nonlinear semipositone fractional q q-difference equations with q q-integral boundary conditions

“…In [3,[19][20][21], the authors had adopted the similar conditions of (1.2) to obtain various existence theorems of positive solutions for some semipositone fractional boundary value problems.…”

“…In this work we study the following system of nonlinear semipositone fractional q-difference equations with q-integral boundary conditions where α ∈ (2, 3), ν ∈ (1, 2) are real numbers, D α q is the Riemann-Liouville's fractional q-derivative of order α, and the nonnegative constant β, and the functions f i (i = 1, 2) satisfy the conditions (H1) β 0 and 1 − β Recently, there are a large number of papers involving fractional differential equations in the literatures, for example, we refer the readers to [1][2][3][4][5][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the references therein. In [7,14] and they obtained the existence of positive solutions by the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.…”

Unique solutions for a new coupled system of fractional differential equations

“…Different boundary conditions of coupled systems can be found in the discussions of some problems such as Sturm-Liouville problems and some reaction-diffusion equations (see [26,27]), and they have some applications in many fields such as mathematical biology (see [28,29]), natural sciences and engineering; for example, we can see beam deformation and steady-state heat flow [30,31] and heat equations [14,32,33]. So nonlinear coupled systems subject to different boundary conditions have been paid much attention to, and the existence or multiplicity of solutions for the systems has been given in literature, see [4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24][25] for example. The usual methods used are Schauder's fixed point theorem, Banach's fixed point theorem, Guo-Krasnosel'skii's fixed point theorem on cone, nonlinear differentiation of Leray-Schauder type and so on.…”

Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations

“…In recent years, there have been some significant developments in the study of ordinary differential equations and partial differential equations involving fractional derivatives with coupled boundary conditions, as shown by the papers [26,27,32,38,42,43] and the references therein. For example, by mixed monotone method, Cui et al [15] established sufficient conditions for the existence and uniqueness of positive solutions to a singular differential system with integral boundary value conditions.…”