In this paper we consider the Cauchy boundary value problem for the integro-differential equation utt −m ( ∫

We present a probabilistic construction of $\mathbb{R}^d$ -valued non-linear affine processes with jumps. Given set $\Theta$ parameters, we define family sublinear expectations on the Skorokhod space under which canonical process X is (sublinear) Markov generator. This yields tractable model for Knightian uncertainty expectation Markovian functional can be calculated via partial integro-differe...

Abstract In light of recent work on particles fluctuating in linear viscoelastic fluids, we study a stochastic partial-integro-differential equation with memory that is driven by stationary noise bounded, smooth domain. Using the framework generalized solutions introduced McKinley and Nguyen (SIAM J Math Anal 50(5):5119–5160, 2018), provide conditions differential operator to obtain existence a...

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often ...

In this paper, we extend the classical Lie symmetry analysis from partial differential equations to integro-differential equations with functional derivatives. We continue the work of Oberlack and Wacławczyk (2006, Arch. Mech. 58, 597), (2013, J. Math. Phys. 54, 072901), where the extended Lie symmetry analysis is performed in the Fourier space. Here, we introduce a method to perform the extend...

The present study is an attempt to find a solution for Volterra's Population Model by utilizing Spectral methods based on Rational Christov functions. Volterra's model is a nonlinear integro-differential equation. First, the Volterra's Population Model is converted to a nonlinear ordinary differential equation (ODE), then researchers solve this equation (ODE). The accuracy of method is tested i...

The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-difference equations. Our method depends mainly on a Taylor expansion approach. This method transforms mixed linear integro-differentialdifference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability a...

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markovswitching jump-diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic progr...

Abstract We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here are abstract partial-differential algebraic considered in Hilbert spaces. The catch is to consider time-dependent partial differential an exponentially weighted space. In passing, one establishes time derivative as a continuously invertible, normal operator admitting functional ...

In this paper, a numerical method is proposed to solve FredholmVolterra fractional integro-differential equation with nonlocal boundary conditions. For this purpose, the Chebyshev wavelets of second kind are used in collocation method. It reduces the given fractional integro-differential equation (FIDE) with nonlocal boundary conditions in a linear system of equations which one can solve easily...