Existence and uniqueness of positive solutions for boundary value problems of fractional differential equations

Abstract

By using fixed point results of mixed monotone operators on cones and the concept of ?-concavity, we study the existence and uniqueness of positive solutions for some nonlinear fractional differential equations via given boundary value problems. Some concrete examples are also provided illustrating the obtained results.

Existence of solutions of a non-variational bi-harmonic system via fixed point theory

“…Existence, non existence, and a priori estimates for solutions are addressed in many papers [2], [4], [5] and [15]. Similar results are obtained for the bi-Laplacian systems, fractional differential equations and nonlinear elastic beam equations using topological methods, namely fixed point theorem and degree theory [1], [7], [10], [11], [13], [18].…”

Nonlinear sum operator equations and applications to elastic beam equation and fractional differential equation

“…Because of non-local behavior, fractional order boundary value problems are extensively applied to blood flow problems, control theory, the fluid-dynamic traffic model and polymer rheology. It implies that differential operators of arbitrary order can describe memory and hereditary properties of certain important processes [28][29][30][31]. There are many tools to deal with the uniqueness and multiplicity of solutions for fractional differential equations such as mixed monotone operators [23,[32][33][34], Avery-Peterson fixed point theorem [35,36], Guo-Krasnosel'skii fixed point theorem on a cone [37,38], the fixed point index theory [39][40][41], monotone iteration method [42], the critical point theory [43,44], Schauder's fixed point theory [45] and stability.…”

Littlewood-Paley g-function and Radon Transform on the Heisenberg Group

“…As we know, T n is studied in fractional differential equations due to its wide applications (see [1,14,15]). In this paper, Combining with these hyperplanes and T n we have the following definition.…”