Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Differential Equations with Antiperiodic Boundary Conditions

This paper studies the existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations of order α,β∈(4,5] with antiperiodic boundary conditions. Our results are based on the nonlinear alternative of Leray-Schauder type and the contraction mapping principle. Two illustrative examples are also presented

Existence of solutions for fractional differential inclusions with nonlocal strip conditions

AbstractIn this paper, we discus the existence of solutions for a nonlocal boundary value problem of fractional differential inclusions concerning a nonlocal strip condition via some fixed point theorems. Our results include the cases when the right-hand side of the inclusion is convex as well as nonconvex valued

A Study of Nonlinear Fractional q

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional q-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples

Piecewise polynomial collocation for linear boundary value problems of fractional differential equations

AbstractWe consider a class of boundary value problems for linear multi-term fractional differential equations which involve Caputo-type fractional derivatives. Using an integral equation reformulation of the boundary value problem, some regularity properties of the exact solution are derived. Based on these properties, the numerical solution of boundary value problems by piecewise polynomial collocation methods is discussed. In particular, we study the attainable order of convergence of proposed algorithms and show how the convergence rate depends on the choice of the grid and collocation points. Theoretical results are verified by two numerical examples

On the Dimension of the Solution Set for Semilinear Fractional Differential Inclusions

We investigate the existence and dimension of the solution set for a nonlocal problem of semilinear fractional differential inclusions. The main tools of our study include some well-known results on multivalued maps

The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem in Ω={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ} such that y|[0,b] is continuous and ℬ is a phase space

Existence Results for a Riemann-Liouville-Type Fractional Multivalued Problem with Integral Boundary Conditions

We discuss the existence of solutions for a boundary value problem of Riemann-Liouville fractional differential inclusions of order ∈ (2, 3] with integral boundary conditions. We establish our results by applying the standard tools of fixed point theory for multivalued maps when the right-hand side of the inclusion has convex as well as nonconvex values. An illustrative example is also presented

Generalized Antiperiodic Boundary Value Problems for the Fractional Differential Equation with p-Laplacian Operator

We discuss the existence of solutions about generalized antiperiodic boundary value problems for the fractional differential equation with p-Laplacian operator , , , , , , where is the Caputo fractional derivative, , , , and , , , . Our results are based on fixed point theorem and contraction mapping principle. Furthermore, three examples are also given to illustrate the results