Numerical simulation for time fractional integro partial differential equations arising in viscoelastic dynamical system

Abstract

The study on fractional calculus gains more attention of many researchers in recent times, due to its immense applicability to define various models, such as viscoelastic damped structure [1], the model due to radiative transfer [2], the theory of linear transport [3], and the mathematical structure due to kinetic energy of gases [4]. A detailed investigation about the application of fractional differential as well as fractional integro-differential equation is available in [5–7]. The general form of a fractional derivative viscoelastic models can be written as: 8.1 https://www.w3.org/1998/Math/MathML" display="block"> X ( t ) + ∑ m = 1 M a m D t α m X ( t ) = E 0 Y ( t ) + ∑ n = 1 N E n D t β n Y ( t ) , https://www.w3.org/1999/xlink" xlink:href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003328032/39998614-bd30-4270-a56c-d58717d36a18/content/math8_1.tif"/>