Qualitative theory and approximate solution to a dynamical system under modified type Caputo-Fabrizio derivative

Eiman; Saowaluck Chasreechai; Thanin Sitthiwirattham; M. A. El-Shorbagy; Muhammad Sohail; Ubaid Ullah; Mati ur Rahman; Eiman; Saowaluck Chasreechai; Thanin Sitthiwirattham; M. A. El-Shorbagy; Muhammad Sohail; Ubaid Ullah; Mati ur Rahman

doi:10.3934/math.2022792

AIMS Mathematics

2022, Volume 7, Issue 8: 14376-14393. doi: 10.3934/math.2022792

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Qualitative theory and approximate solution to a dynamical system under modified type Caputo-Fabrizio derivative

1.
Department of Mathematics, University of Malakand, Chakdara Dir(L), KPK, Pakistan
2.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand
3.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
4.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
5.
Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt
6.
School of Mathematical Science, Shanghai Jiao Tong University, Shanghai China

Received: 12 March 2022 Revised: 10 May 2022 Accepted: 12 May 2022 Published: 06 June 2022
MSC : 26A33, 35A02, 35A25

Qualitative theory, together with approximate solutions to a dynamic system, are investigated. The proposed mathematical model is composed of protected, susceptible, infected and treated classes. The adopted model expresses the mechanism of disease due to Typhoid fever. A modified type Caputo-Fabrizio fractional derivative (CFFD) is considered for the intended results. With the help of fixed point theory, some sufficient conditions for the existence of approximate solutions are developed. Also, to compute an approximate solution with respect to each compartment, we utilize the Laplace Transform and the Adomian decomposition method (ADM). A graphical presentation corresponding to some fundamental data is given.
- dynamical system,
- approximate solution,
- ADM,
- CFFD
Citation: Eiman, Saowaluck Chasreechai, Thanin Sitthiwirattham, M. A. El-Shorbagy, Muhammad Sohail, Ubaid Ullah, Mati ur Rahman. Qualitative theory and approximate solution to a dynamical system under modified type Caputo-Fabrizio derivative[J]. AIMS Mathematics, 2022, 7(8): 14376-14393. doi: 10.3934/math.2022792

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Abstract

Qualitative theory, together with approximate solutions to a dynamic system, are investigated. The proposed mathematical model is composed of protected, susceptible, infected and treated classes. The adopted model expresses the mechanism of disease due to Typhoid fever. A modified type Caputo-Fabrizio fractional derivative (CFFD) is considered for the intended results. With the help of fixed point theory, some sufficient conditions for the existence of approximate solutions are developed. Also, to compute an approximate solution with respect to each compartment, we utilize the Laplace Transform and the Adomian decomposition method (ADM). A graphical presentation corresponding to some fundamental data is given.

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