Abstract
Fractional variational iteration method (FVIM) is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method (FVIM) was extended to derive analytical solutions in the form of a series for these equations. The behavior of the solutions and the effects of different values of fractional order 𝛼 are indicated graphically. The results obtained by the FVIM reveal that the method is very reliable, convenient, and effective method for nonlinear differential equations with modified Riemann-Liouville derivative
Highlights
In recent years, fractional calculus used in many areas such as electrical networks, control theory of dynamical systems, probability and statistics, electrochemistry of corrosion, chemical physics, optics, engineering, acoustics, viscoelasticity, material science and signal processing can be successfully modelled by linear or nonlinear fractional order differential equations 1–10
We extend the application of the VIM in order to derive analytical approximate solutions to nonlinear fractional Riccati differential equation: D∗αyxAxBxyxCx y2 x, x ∈ R, 0 < α ≤ 1, t > 0, 1.1 subject to the initial conditions y k 0 dk, k 0, 1, 2, . . . , n − 1, 1.2 where α is fractional derivative order, n is an integer, A x, B x, and C x are known real functions, and dk is a constant
The goal of this paper is to extend the application of the variational iteration method to solve fractional nonlinear Riccati differential equations with modified Riemann-Liouville derivative
Summary
Fractional calculus used in many areas such as electrical networks, control theory of dynamical systems, probability and statistics, electrochemistry of corrosion, chemical physics, optics, engineering, acoustics, viscoelasticity, material science and signal processing can be successfully modelled by linear or nonlinear fractional order differential equations 1–10. The goal of this paper is to extend the application of the variational iteration method to solve fractional nonlinear Riccati differential equations with modified Riemann-Liouville derivative. The conclusions are given in the final Section 5
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