First order integro-differential equations in Banach algebras involving Caratheodory and discontinuous nonlinearities

First-Order Singular and Discontinuous Differential Equations

Impulsive Discontinuous Hyperbolic Partial Differential Equations of Fractional Order on Banach Algebras

This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Carathéodory conditions and certain monotonicity conditions.

Stabilization and controllability of first-order integro-differential hyperbolic equations

In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prov...

Impulsive Boundary-value Problems for First-order Integro-differential Equations

This article concerns boundary-value problems of first-order nonlinear impulsive integro-differential equations: y′(t) + a(t)y(t) = f(t, y(t), (Ty)(t), (Sy)(t)), t ∈ J0, ∆y(tk) = Ik(y(tk)), k = 1, 2, . . . , p,

Dhage iteration method for PBVPs of nonlinear first order hybrid integro-differential equations

In this paper, author proves the algorithms for the existence as well as the approximation of solutions to a couple of periodic boundary value problems of nonlinear first order ordinary integro-differential equations using operator theoretic techniques in a partially ordered metric space. The main results rely on the Dhage iteration method embodied in the recent hybrid fixed point theorems of D...