Model of Break-Bone Fever via Beta-Derivatives

Abstract

Using the new derivative called beta-derivative, we modelled the well-known infectious disease called break-bone fever or the dengue fever. We presented the endemic equilibrium points under certain conditions of the physical parameters included in the model. We made use of an iteration method to solve the extended model. To show the efficiency of the method used, we have presented in detail the stability and the convergence of the method for solving the system (2). We presented the uniqueness of the special solution of system (2) and finally the numerical simulations were presented for various values of beta.

A remark on local fractional calculus and ordinary derivatives

“…For example, taking k.t/ D t and a D 0, we get the definition from [7,8,10,11,13] (also called conformable fractional derivative); when k.t / D t a, the one from [1,2,18]; for k.t / D t C 1= .˛/, the definition in [4,5].…”

Three-Point Boundary Value Problems for Conformable Fractional Differential Equations

“…We now obtain Green's function corresponding to the fractional differential equations (11) of order + 1 with 1 < ≤ 2 subject to boundary conditions (2). By changing the order of integration, we note that…”

“…where D is the conformable fractional derivative of order ∈ (1,2], D is the ordinary derivative, : [0, 1] × R → R is a known continuous function, and are real numbers, > 0, and ∈ (0, 1). Fractional calculus and fractional differential equations are relevant areas of research.…”

“…Fractional calculus and fractional differential equations are relevant areas of research. There are several concepts of fractional derivatives, some classical, such as RiemannLiouville or Caputo definitions, and some novel, such as conformable fractional derivative [1], -derivative [2], or a new definition [3,4]. The relation between these definitions and their potential applications needs further study.…”

A numerical algorithm for the solution of nonlinear fractional differential equations via beta‐derivatives

“…They found the reproductive number and the steady state by analyzing this model. The susceptible‐exposed‐infected (SEI) model of the breakbone disease has been studied in Atangana and Oukouomi Noutchie . The solution of the constructed system was investigated by using homotopy decomposition method.…”