Existence Results for Nonlinear Fractional Difference Equation
نویسندگان
چکیده
This paper is concerned with the initial value problem to a nonlinear fractional difference equation with the Caputo like difference operator. By means of some fixed point theorems, global and local existence results of solutions are obtained. An example is also provided to illustrate our main result.
منابع مشابه
Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation
This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.
متن کاملA distinct numerical approach for the solution of some kind of initial value problem involving nonlinear q-fractional differential equations
The fractional calculus deals with the generalization of integration and differentiation of integer order to those ones of any order. The q-fractional differential equation usually describe the physical process imposed on the time scale set Tq. In this paper, we first propose a difference formula for discretizing the fractional q-derivative of Caputo type with order and scale index . We es...
متن کاملPositive solutions for discrete fractional initial value problem
In this paper, the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement .The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...
متن کاملExistence of Mild Solutions to a Cauchy Problem Presented by Fractional Evolution Equation with an Integral Initial Condition
In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.
متن کاملNew existence results for a coupled system of nonlinear differential equations of arbitrary order
This paper studies the existence of solutions for a coupled system of nonlinear fractional differential equations. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.
متن کامل