Functional differential equations with nonlocal initial conditions

Impulsive Functional-differential Equations with Nonlocal Conditions

Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions

We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the pa...

Semilinear Volterra Integrodifferential Equations with Nonlocal Initial Conditions

where h ∈ L1(0,T ;X) and f : [0,T ]×X →X. This is obtained if one takes F(u)(t)= h(t)−∫ t 0 a(t−s)f (s,u(s))ds in (1.1). Such problems are important from the viewpoint of applications since they cover nonlocal generalizations of integrodifferential equations arising in the mathematical modeling of heat conduction in materials with memory. Byszewski [6, 7] initiated the work concerning abstract ...

Solutions of Two-term Time Fractional Order Differential Equations with Nonlocal Initial Conditions

We study the existence of mild solutions for the two-term fractional order abstract differential equation Dα+1 t u(t)+ μD β t u(t)−Au(t) = D α−1 t f (t,u(t)), t ∈ [0,1], 0 < α ≤ β ≤ 1, μ ≥ 0, with nonlocal initial conditions and where A is a linear operator of sectorial type. To achieve our goal, we use a new mixed method, which combines a generalization of the theory of C0semigroups, Hausdorff...

Mild Solutions for Fractional Differential Equations with Nonlocal Conditions

This paper is concerned with the existence and uniqueness of mild solution of the fractional differential equations with nonlocal conditions d q xt/dt q −Axt ft, xt, Gxt, t ∈ 0, T, and x0 gx x 0 , in a Banach space X, where 0 < q < 1. General existence and uniqueness theorem, which extends many previous results, are given.