Abstract
Abstract In this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.
Highlights
Fractional calculus, which includes arbitrary order derivatives and integrals, is the generalized form of the classical calculus. It has been frequently researched by many scientists to model real world problems. It offered a decent way of implementation for plenty of models in miscellaneous areas of engineering and physics such as, electrical networks [9], fluid flow [11], image and signal processing [17], mathematical physics [30], viscoelasticity [25], biology [20], control [5] and see references therein [31,32,33,34,35,36,37,38,39,40,41,42,43,44]
It is observed that the exp-function method appears to be a robust and adequate tool for handling of fractional partial differential equations (FPDEs)
Comparison of the approximate solutions obtained by perturbation-iteration algorithm (PIA) for α = 0.75, α = 0.85 and α = 0.95 reveals the power and fast convergence rate of the method even after a few approximations
Summary
Fractional calculus, which includes arbitrary order derivatives and integrals, is the generalized form of the classical calculus. It has been frequently researched by many scientists to model real world problems. Seeking analytical and approximate solutions of fractional partial differential equations (FPDEs) become more popular. We use exp-function method [15] and perturbation-iteration algorithm (PIA) [27,28,29] to present new analytical and numerical solutions of fractional coupled Burgers’ equations given as [24]: Dtα u. The exp-function method is a robust technique for obtaining compacton-like, periodic and solitary solutions of FPDEs. It transforms the given system to an ordinary differential equation and yields to solve it efficiently.
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