Well-posed conditions on a class of fractional q-differential equations by using the Schauder fixed point theorem

In this paper, we propose the conditions on which a class of boundary value problems, presented by fractional q-differential equations, is well-posed. First, under the suitable conditions, we will prove the existence and uniqueness of solution by means of the Schauder fixed point theorem. Then, the stability of solution will be discussed under the perturbations of boundary condition, a function existing in the problem, and the fractional order derivative. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.

An Existence Result for a Class of Coupled Polyharmonic Systems

This work deals with the existence of positive continuous solutions for a nonlinear coupled polyharmonic system. Our analysis is based on some potential theory tools, properties of functions in the Kato class Km, n and the Schauder fixed point theorem.

Existence of solutions for fractional order impulsive differential equations with integral boundary conditions

In this paper, we prove the expression and the existence of a class of nonlinear impulsive fractional order differential equations with integral boundary conditions. The unique solution of the differential equations by Green’s function is given. By using Schauder fixed point theorem and Leray-Schauder fixed point theorem, several sufficient conditions for the existence and uniqueness results are established.

The continuation of solutions to systems of Caputo fractional order differential equations

In this paper, we study the continuation of solutions to systems of Caputo fractional order differential equations. The continuation is constructed and proven by using the Schauder Fixed Point Theorem. As a necessary prerequisite to the continuation, the existence and uniqueness results generalized for systems are also reviewed.

Existence of solutions for a coupled system with ∅-Laplacian operators and nonlinear coupled boundary conditions

We study the existence of solutions of the system submitted to nonlinear coupled boundary conditions on [0, T] where ∅1, ∅2: (-a, a) → ℝ, with 0 < a < +∞, are two increasing homeomorphisms such that ∅1(0) = ∅2(0) = 0, and fi : [0, T] × ℝ4 → ℝ, i ∈{1, 2} are two L1-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.