Stability in Nonlinear Neutral Caputo q-Fractional Difference Equations

Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions

Since Al-Salam [1] and Agarwal [2] introduced the fractional q-difference calculus, the theory of fractional q-difference calculus itself and nonlinear fractional q-difference equation boundary value problems have been extensively investigated by many researchers. For some recent developments on fractional q-difference calculus and boundary value problems of fractional q-difference equations, s...

A Krasnoselskii Existence Result For Nonlinear Delay Caputo q—Fractional Difference Equations With Applications to Lotka—Volterra Competition Model∗

In this paper, we investigate the existence of solutions for nonlinear delay Caputo q—fractional difference equations. The main result is proved by means of Krasnoselskii’s fixed point theorem. As an application, we link the conclusion of the main theorem to an existence result for Lotka—Volterra model.

Initial time difference quasilinearization for Caputo Fractional Differential Equations

Correspondence: [email protected]. tr Department of Statistics, Gaziosmanpasa University, Tasliciftlik Campus, 60250 Tokat, Turkey Abstract This paper deals with an application of the method of quasilinearization by not demanding the Hölder continuity assumption of functions involved and by choosing upper and lower solutions with initial time difference for nonlinear Caputo fractional different...

Fixed points and asymptotic stability of nonlinear fractional difference equations

In this paper, we discuss nonlinear fractional difference equations with the Caputo like difference operator. Some asymptotic stability results of equations under investigated are obtained by employing Schauder fixed point theorem and discrete Arzela-Ascoli’s theorem. Three examples are also provided to illustrate our main results.

Asymptotic Stability Results for Nonlinear Fractional Difference Equations