Nonlocal Parabolic Integro-differential Equations with Delays

Regularity estimates for parabolic integro- differential equations and applications

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...

The Generalized Quasilinearization Method for Parabolic Integro-differential Equations

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

Linear Complexity Solution of Parabolic Integro-differential Equations

The numerical solution of parabolic problems ut + Au = 0 with a pseudodifferential operator A by wavelet discretization in space and hp discontinuous Galerkin time stepping is analyzed. It is proved that an approximation for u(T ) can be obtained in N points with accuracy O(N) for any integer p ≥ 1 in work and memory which grows logarithmically-linear in N .

Integro-differential Equations of Fractional Order with Nonlocal Fractional Boundary Conditions Associated with Financial Asset Model

In this article, we discuss the existence of solutions for a boundaryvalue problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented. 1. Formulation ...

Nonlinear Integro - Differential Equations