Analytical and approximate solutions of fractional‐order susceptible‐infected‐recovered epidemic model of childhood disease

Abstract

In this work, we make use of the conformable fractional differential transform method (CFDTM) in order to compute an approximate solution of the fractional-order susceptible-infected-recovered (SIR) epidemic model of childhood disease. The method provides the solution in the form of a rapidly convergent series. Two explanatory and illustrative examples are given to represent the efficacy of the obtained results. KEYWORDS childhood disease, conformable fractional differential transform method (CFDTM), fractional-order susceptible-infected-recovered (SIR) epidemic model, fractional power series, Liouville-Caputo fractional derivative Math Meth Appl Sci. 2019;42:935-941.wileyonlinelibrary.com/journal/mma

Generalization of Caputo-Fabrizio Fractional Derivative and Applications to Electrical Circuits

“…In the recent decades, the theory of fractional calculus has brought the attention of a great number of researchers in various disciplines. Indeed, it was observed that the use of fractional derivatives is very useful for modeling many problems in engineering sciences (see e.g., [1][2][3][4][5][6][7][8][9][10]). Various notions of fractional derivatives exist in the literature.…”

Dynamical Analysis of Corona-virus (COVID−19) Epidemic Model by Differential Transform Method

“…The concept of differential transform method was first proposed by Zhou [33] in 1986 and it was applied to solve linear and non-linear initial value problems in electric circuit analysis and later it was used to solve linear and non-linear initial value problems, boundary value problems, fractional order derivative problems, fluid flow models and so on, one can refer [1,5,12,15,21,23,24,26,27,29] and references therein for history and properties of DTM. Also, at the present time, this method get much attention to solve SIS (susceptible-infectedsusceptible) and SI (susceptible-infected) epidemic models [2,3], SIR (susceptible-infectedrecovered) epidemic models [16,28], influenza epidemic model [18], compartmental models [7], transmission of seasonal diseases model [4], analysis of computer virus propagation model [24], the transmission dynamical of syphilis disease model [17], SEIR (susceptible-exposed -infectedrecovered) epidemic model [14], SAEIQRS (susceptible-antidotal-exposed-infected-quarantinedrecovered-susceptible) model [8] and for HBV infection model [?, 11], also one can refer the references therein for more details. To speak about the advantages and generic nature of the DTM, it is worthwhile to mention that the method can be applied to linear and nonlinear ODEs not requiring discretization, linearization or perturbation.…”

A New Subclass of Analytic Functions Defined by Using Salagean q-Differential Operator

“…Till now, only non-significant interest in this area has been shown, although it deserves more attention. Many differential and integral operators can be written in terms of convolution; for detail, we refer to [25][26][27][28][29][30]. It is worth mentioning that the technique of convolution helps researchers in further investigation of the geometric properties of analytic functions.…”