A note on the fractional Cauchy problems with nonlocal initial conditions

AbstractOf concern is the Cauchy problems for fractional integro-differential equations with nonlocal initial conditions. Using a new strategy in terms of the compactness of the semigroup generated by the operator in the linear part and approximating technique, a new existence theorem for mild solutions is established. An application to a fractional partial integro-differential equation with a nonlocal initial condition is also considered

Existence of Mild Solutions for Fractional Nonlocal Evolution Equations With Delay in Partially Ordered Banach Spaces

This paper deals with the existence of mild solutions for the abstract fractional nonlocal evolution equations with noncompact semigroup in partially ordered Banach spaces. Under some mixed conditions, a group of sufficient conditions for the existence of abstract fractional nonlocal evolution equations are obtained by using a Krasnoselskii type fixed point theorem. The results we obtained are a generalization and continuation of the recent results on this issue. At the end, an example is given to illustrate the applicability of abstract result

The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1<α<2

AbstractThis paper is mainly concerned with the existence of mild solutions for fractional differential equations with nonlocal conditions of order 1<α<2. The results are obtained by the fixed point theorem combined with solutions operator theorems

Existence and Uniqueness of Positive Solutions for a Fractional Switched System

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0, t∈J=[0,1]); (u(0)=u′′(0)=0,u(1)=∫01u(s) ds), where Dc0+α is the Caputo fractional derivative with 2<α≤3, σ(t):J→{1,2,…,N} is a piecewise constant function depending on t, and ℝ+=[0,+∞),  fi,gi∈C[J×ℝ+,ℝ+], i=1,2,…,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results

Generalized Antiperiodic Boundary Value Problems for the Fractional Differential Equation with p-Laplacian Operator

We discuss the existence of solutions about generalized antiperiodic boundary value problems for the fractional differential equation with p-Laplacian operator , , , , , , where is the Caputo fractional derivative, , , , and , , , . Our results are based on fixed point theorem and contraction mapping principle. Furthermore, three examples are also given to illustrate the results

Book of Abstracts

USPCAPESFAPESPCNPqINCTMatICMC Summer Meeting on Differentail Equations.\ud São Carlos, Brasil. 3-7 february 2014