Analysis of a fractional epidemic model by fractional generalised homotopy analysis method using modified Riemann - Liouville derivative

• Published in: Applied Mathematical Modelling Vol. 92; pp. 525 - 545
• Main Authors: Saratha, S.R., Sai Sundara Krishnan, G., Bagyalakshmi, M.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.04.2021; Elsevier BV
• Subjects: Derivatives; Epidemic model; Epidemics; Fractional [formula omitted]-transform; Fractional calculus; Integral transforms; Integrals; Mittag-Leffler function; Modified Riemann - Liouville derivative; Nonlinear differential equations; Fractional G-transform; Modified Riemann - Liouville derivative; Epidemic model; Mittag-Leffler function; Fractional calculus
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.11.019

•A fractional generalized integral transform with modified Riemann Liouville derivative is devised.•A hybrid fractional generalized homotopy analysis method is developed.•The new method, known as MRFGHAM, avoids iterative differentiation and integration.•Applicability of MRFGHAM to solve fractional epidemic model is demonstrated.•The results of MRFGHAM yield an excellent agreement with those from the other existing methods. This paper proposes the notion of a fractional generalised integral transform (Fractional G-transform) using modified Riemann-Liouville derivative with the Mittag-Leffler function as a kernel. We investigate the basic properties of the Fractional G-transform. In addition, the homotopy analysis is incorporated to introduce a hybrid Fractional Generalised Homotopy Analysis Method using Modified Riemann-Liouville Derivative, which is denoted as MRFGHAM. We highlight the merits of MRFGHAM and apply it to solve fractional nonlinear differential equations. The proposed method is implemented to formulate a fractional non-fatal disease epidemic model and to obtain the results of a spreading process subject to various settings of the fractional parameters. We also statistically validate the variations in the spread of the non-fatal disease obtained at different stages. Furthermore, the fractional power epidemic model is reduced to a simple epidemic model, and the obtained results indicate an excellent agreement with those of existing conventional methods.