Optimal Perturbation Iteration Method for Solving Fractional Model of Damped Burgers’ Equation

Abstract

The newly constructed optimal perturbation iteration procedure with Laplace transform is applied to obtain the new approximate semi-analytical solutions of the fractional type of damped Burgers’ equation. The classical damped Burgers’ equation is remodeled to fractional differential form via the Atangana–Baleanu fractional derivatives described with the help of the Mittag–Leffler function. To display the efficiency of the proposed optimal perturbation iteration technique, an extended example is deeply analyzed.

A new efficient technique for solving modified Chua’s circuit model with a new fractional operator

“…Deniz and Bildik presented the optimal perturbation iteration algorithms (OPIA) in 2016 [43]. It has been proven that these algorithms can be safely applied to many types of differential equations [44][45][46][47][48][49][50][51][52]. In this section, we give a short description of OPIA for systems of ordinary differential equation.…”

“…This technique has been applied to many types of ODEs and PDEs such as Bratu-type [43], Riccati differential equation [44], heat transfer equations [45], nonlinear systems [46], Lane-Emden types [47], generalized regularized long wave equations [48]. More studies can also be found in [49][50][51][52][53][54][55][56][57]. The rest of the current paper is planned as follows.…”

Approximate solution of the electrostatic nanocantilever model via optimal perturbation iteration method

“…Other important models including system of nonlinear coupled differential equations occurring in the phenomenon of fluid, 16,17 nonconservative dynamical system of a rotating electrical machine, 18 strongly nonlinear equation, 19‐21 delay differential equation, 22 nonlinear heat transfer equations, 23 Lane‐Emden‐type equations, 24,25 Fisher's equations, 26 Bratu‐type problems, 27 generalized regularized long wave equations, 28 Burgers's equation, 29 modified Boussinesq‐Burger equations, 30 coupled Drinfel'd‐Sokolov‐Wilson equation, 31 and Klein‐Gordon equations 32 . Other models that have been solved using this method can be found in References 33‐37 and references therein.…”