Nonlinear qq-fractional differential equations with nonlocal and sub-strip type boundary conditions

This paper is concerned with new boundary value problems of nonlinear $q$-fractional differential equations with nonlocal and sub-strip type boundary conditions. Our results are new in the present setting and rely on the contraction mapping principle and a fixed point theorem due to O'Regan. Some illustrative examples are also presented

An Existence Theorem for Fractional q

By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example

On Nonlinear Fractional Sum-Difference Equations via Fractional Sum Boundary Conditions Involving Different Orders

We study existence and uniqueness results for Caputo fractional sum-difference equations with fractional sum boundary value conditions, by using the Banach contraction principle and Schaefer’s fixed point theorem. Our problem contains different numbers of order in fractional difference and fractional sums. Finally, we present some examples to show the importance of these results

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

Existence and rapid convergence results for nonlinear Caputo nabla fractional difference equations

This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results

CONVERGENCE OF APPROXIMATE SOLUTIONS TO NONLINEAR CAPUTO NABLA FRACTIONAL DIFFERENCE EQUATIONS WITH BOUNDARY CONDITIONS

This article studies a boundary value problem for a nonlinear Ca- puto nabla fractional difference equation. We obtain quadratic convergence results for this equation using the generalized quasi-linearization method. Fur- ther, we obtain the convergence of the sequences is potentially improved by the Gauss-Seidel method. A numerical example illustrates our main results

Solvability for a Discrete Fractional Three-Point Boundary Value Problem at Resonance

This paper is concerned with the existence of solutions to a discrete three-point boundary value problem at resonance involving the Riemann-Liouville fractional difference of order α∈(0,1]. Under certain suitable nonlinear growth conditions imposed on the nonlinear term, the existence result is established by using the coincidence degree continuation theorem. Additionally, a representative example is presented to illustrate the effectiveness of the main result

Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions

In this article we discuss some of the qualitative properties of fractional difference operators. We especially focus on the connections between the fractional difference operator and the monotonicity and convexity of functions. In the integer-order setting, these connections are elementary and well known. However, in the fractional-order setting the connections are very complicated and muddled. We survey some of the known results and suggest avenues for future research. In addition, we discuss the asymptotic behavior of solutions to fractional difference equations and how the nonlocal structure of the fractional difference can be used to deduce these asymptotic properties