Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

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.

On Riemann—Liouville and Caputo Fractional Forward Difference Monotonicity Analysis

“…which is the required Equation (6). Using the same technique used for Equation ( 6), we can prove Equation ( 7), and thus, the proof is completed.…”

“…Fractional differentiation and integration have opened many new doors for researchers in recent decades due to their wide and novel applicability in many fields of science including mathematical analysis, technology, and engineering (see [1][2][3][4][5][6][7]). Many techniques are used to deal with these new differential and integral operators; for instance, some researchers used analytical techniques including Laplace transform, spline interpolation, Green function, Crank-Nicolson approximation method, method of separation of variable, and many others to derive exact solutions to linear differential or integral equations (see [8][9][10][11][12][13][14]).…”

Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations

“…In the last few years, researchers introduced various models involving fractional derivative and integral operators of arbitrary order (see [10]). Some recent contributions to the theory of fractional differential (or difference) equations and its applications can be found in [11][12][13][14][15][16][17] and references therein.…”

An Efficient Method Based on Framelets for Solving Fractional Volterra Integral Equations

“…Most recently, numerous scientists provided new definitions of fractional order derivatives and integrals that opened a new era in the history of fractional derivatives, such as the Atangana–Baleanu fractional integral [ 1 ], the Caputo fractional derivative [ 2 ] and the Caputo–Fabrizio fractional derivative [ 3 ]. There is a series of new lines of research that is devoted to fractional calculus and its applications in many disciplines, such as physics, engineering and modeling [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ].…”