Numerical Solutions for Time-Fractional Cancer Invasion System With Nonlocal Diffusion

J. Manimaran; L. Shangerganesh; Amar Debbouche; Valery Antonov

doi:10.3389/fphy.2019.00093

Frontiers in Physics (Jul 2019)

Numerical Solutions for Time-Fractional Cancer Invasion System With Nonlocal Diffusion

J. Manimaran,
L. Shangerganesh,
Amar Debbouche,
Valery Antonov

Affiliations

J. Manimaran: Department of Applied Sciences, National Institute of Technology Goa, Goa, India
L. Shangerganesh: Department of Applied Sciences, National Institute of Technology Goa, Goa, India
Amar Debbouche: Department of Mathematics, Guelma University, Guelma, Algeria
Valery Antonov: Department of Mathematics, Peter the Great Saint Petersburg Polytechnic University, Saint Petersburg, Russia

DOI: https://doi.org/10.3389/fphy.2019.00093
Journal volume & issue: Vol. 7

Abstract

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This article studies the existence and uniqueness of a weak solution of the time-fractional cancer invasion system with nonlocal diffusion operator. Existence and uniqueness results are ensured by adapting the Faedo-Galerkin method and some a priori estimates. Further, finite element numerical scheme is implemented for the considered system. Finally, various numerical computations are performed along with the convergence analysis of the scheme.

Published in Frontiers in Physics

ISSN: 2296-424X (Online)
Publisher: Frontiers Media S.A.
Country of publisher: Switzerland
LCC subjects: Science: Physics
Website: https://www.frontiersin.org/journals/physics

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