On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method

Dumitru Baleanu; Seher Melike Aydogn; Hakimeh Mohammadi; Shahram Rezapour

Alexandria Engineering Journal (Oct 2020)

On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method

Dumitru Baleanu,
Seher Melike Aydogn,
Hakimeh Mohammadi,
Shahram Rezapour

Affiliations

Dumitru Baleanu: Department of Mathematics, Cankaya University, Ogretmenler Cad. 14 06530, Balgat, Ankara, Turkey; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
Seher Melike Aydogn: Department of Mathematics, Istanbul Technical University, Istanbul, Turkey
Hakimeh Mohammadi: Department of Mathematics, Miandoab Branch, Islamic Azad University, Miandoab, Iran
Shahram Rezapour: Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam; Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran; Corresponding author.

Journal volume & issue: Vol. 59, no. 5
pp. 3029 – 3039

Abstract

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We present a fractional-order epidemic model for childhood diseases with the new fractional derivative approach proposed by Caputo and Fabrizio. By applying the Laplace Adomian decomposition method (LADM), we solve the problem and the solutions are presented as infinite series converging to the solution. We prove the existence, uniqueness, and stability of the solution by using the fixed point theory. Also, we provide some numerical results to illustrate the effectiveness of the new derivative.

Published in Alexandria Engineering Journal

ISSN: 1110-0168 (Print); 2090-2670 (Online)
Publisher: Elsevier
Country of publisher: Egypt
LCC subjects: Technology: Engineering (General). Civil engineering (General)
Website: http://www.journals.elsevier.com/alexandria-engineering-journal/

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