Existence and multiplicity of solutions for nonlinear fractional differential equations, By Hossein Piri

Research

Title	Existence and multiplicity of solutions for nonlinear fractional differential equations
Type	Article
Keywords	Fractional differential equation, positive solution, index fixed point theorem.
Researchers	Seyyed Hamid Reza Merasi، Hossein Piri، Hassen Aydi

Abstract

In this paper, we consider the following fractional initial value problems: Dαu(t) = f(t, u(t), Dβu(t)), t ∈ (0, 1], u (k) (0) = ηk, k = 0, 1, ..., n − 1, where n − 1 < β < α < n, (n ∈ N) are real numbers, Dα and Dβ are the Caputo fractional derivatives and f ∈ C([0, 1] × R). Using the fixed point index theory, we study the existence and multiplicity of positive solutions and obtain some new results. c 2016 All rights reserved.