Preprint Article Version 1 NOT YET PEER-REVIEWED

The Analytical Solution of Parabolic Volterra Integro- Differential Equations in the Infinite Domain

  1. Department of Applied Mathematics , School of sciences, Xi’an University of Technology, Xi’an 710054, China
Version 1 : Received: 11 August 2016 / Approved: 11 August 2016 / Online: 11 August 2016 (11:47:10 CEST)

A peer-reviewed article of this Preprint also exists.

Zhao, Y.; Zhao, F. The Analytical Solution of Parabolic Volterra Integro-Differential Equations in the Infinite Domain. Entropy 2016, 18, 344. Zhao, Y.; Zhao, F. The Analytical Solution of Parabolic Volterra Integro-Differential Equations in the Infinite Domain. Entropy 2016, 18, 344.

Journal reference: Entropy 2016, 18, 344
DOI: 10.3390/e18100344

Abstract

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

Subject Areas

parabolic Volterra integro-differential equations; memory kernel; Laplace transform; Fourier transform; convolution theorem; analytical solution

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