Global existence for functional semilinear integro-differential equations

summary:In this paper, we study the global existence of solutions for first and second order initial value problems for functional semilinear integrodifferential equations in Banach space, by using the Leray-Schauder Alternative or the Nonlinear Alternative for contractive maps

Existence of solutions for fractional differential inclusions with nonlocal strip conditions

AbstractIn this paper, we discus the existence of solutions for a nonlocal boundary value problem of fractional differential inclusions concerning a nonlocal strip condition via some fixed point theorems. Our results include the cases when the right-hand side of the inclusion is convex as well as nonconvex valued

Neumann boundary value problems for impulsive differential inclusions

In this paper, we investigate the existence of solutions for a class of second order impulsive differential inclusions with Neumann boundary conditions. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values

Boundary value problems for nonlinear fractional differential equations and inclusions with nonlocal and fractional integral boundary conditions

This paper studies the boundary value problem of nonlinear fractional differential equations and inclusions of order $q \in (1,2]$ with nonlocal and integral boundary conditions. Some new existence and uniqueness results are obtained by using fixed point theorems

New Existence Results for Fractional Integrodifferential Equations with Nonlocal Integral Boundary Conditions

We consider a boundary value problem of fractional integrodifferential equations with new nonlocal integral boundary conditions of the form: x(0)=βx(θ), x(ξ)=α∫η1‍x(s)ds, and 0<θ<ξ<η<1. According to these conditions, the value of the unknown function at the left end point t=0 is proportional to its value at a nonlocal point θ while the value at an arbitrary (local) point ξ is proportional to the contribution due to a substrip of arbitrary length (1-η). These conditions appear in the mathematical modelling of physical problems when different parts (nonlocal points and substrips of arbitrary length) of the domain are involved in the input data for the process under consideration. We discuss the existence of solutions for the given problem by means of the Sadovski fixed point theorem for condensing maps and a fixed point theorem due to O’Regan. Some illustrative examples are also presented

An Existence Theorem for Fractional q

By employing a nonlinear alternative for contractive maps, we investigate the existence of solutions for a boundary value problem of fractional q-difference inclusions with nonlocal substrip type boundary conditions. The main result is illustrated with the aid of an example