A static mixed boundary value problem of physically nonlinear elasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of an auxiliary linear operator, a non-standard boundary-domain integro-differential formulation of the problem is presented, with respect to the displacements and their gradients. Using a cut-off fu...

In this article, the numerical solution of mixed Volterra–Fredholm integro-differential equations multi-fractional order less than or equal to one in Caputo sense (V-FIFDEs) under initial conditions is presented with powerful algorithms. The method based upon quadrature rule aid finite difference approximation derivative usage collocation points. For treatments, our technique converts V-FIFDEs ...

The work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on uniform mesh utilizing interpolating quadrature rules and exponential basis functions. stability convergence of the proposed discretization technique are analyzed one example is solved to display advantages presented technique.

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...

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...

One of the classical topics in the qualitative theory of differential equations is the Floquet theory. It provides a means to represent solutions and helps in particular for stability analysis. In this paper first we shall study Floquet theory for integro-differential equations (IDE), and then employ it to address stability problems for linear and nonlinear equations.