Solutions For Nonlinear Fractional Differential Equations Research Articles

Multivalued Hardy-Rogers type ЗΘ-contraction and generalized simulation functions

The purpose of this paper is to introduce the notion of multivalued Hardy-Rogers ??-contraction in the sense of generalized simulation functions and to present the corresponding fixed point results with some examples. Moreover, we study the strict fixed point and well-posedness, data dependence, as well as, the Ulam-Hyres stability of the fixed point problem. As an application, we prove the existence of the solution for nonlinear fractional differential equation involving Caputo fractional derivative.

Positive solutions of boundary value problems for p-Laplacian fractional differential equations

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.