On fractional symmetry group scheme to the higher-dimensional space and time fractional dissipative Burgers equation

Abstract

In this paper, we studied a higher-dimensional space and time fractional model, namely, the (3+1)-dimensional dissipative Burgers equation which can be used to describe the shallow water waves phenomena. Here, the analyzed tool is the Lie symmetry scheme in the sense of the Riemann–Liouville fractional derivative. First of all, the symmetry of this considered equation was yielded. Then, based on the above obtained symmetry, the one-parameter Lie group was obtained. Subsequently, this model can be changed into the lower-dimensional equation with the Erdélyi–Kober fractional operators. Lastly, conservation laws of this studied equation via a new conservation theorem were also received. After such a series of processing, these new results play an important role in our understanding of this higher-dimensional space and time differential equations.

Analytical Solutions of the Nonlinear Time-Fractional Coupled Boussinesq-Burger Equations Using Laplace Residual Power Series Technique

“…This definition obtains the same results of C-FD in a very simple way which is more efficient for solving many nonlinear FDEs, see, [51][52][53]. In the future, we attend to solve some new attractive modeling scientific phenomena via L-RPS method using Abu-Shady-Kaabar fractional derivative [51][52][53][54]. Mathematica software 14 is used to compute the numerical and graphical results.…”

“…Moreover, there is a newly proposed fractional derivative definition which is called the "Abu-Shady-Kaabar fractional derivative" and recently introduced by Abu-Shady and Kaabar [51]. This definition obtains the same results of C-FD in a very simple way which is more efficient for solving many nonlinear FDEs, see, [51][52][53]. In the future, we attend to solve some new attractive modeling scientific phenomena via L-RPS method using Abu-Shady-Kaabar fractional derivative [51][52][53][54].…”

Applications of Fuzzy Differential Subordination to the Subclass of Analytic Functions Involving Riemann–Liouville Fractional Integral Operator

“…Using Ruscheweyh and Salagean differential operators, several studies (see, for example, [34]) have generated fuzzy differential subordination. The Riemann-Liouville fractional integral in [35] is used to find the derivative of a Gaussian hypergeometric function and for studying the applications of the fractional integral operator we refer [36][37][38]. The fractional integral in [39] is used to find the derivative of a confluent hypergeometric function.…”

Conservation laws, Lie symmetries, self adjointness, and soliton solutions for the Selkov–Schnakenberg system

“…Partial differential equations (PDEs) play a vital role in the study of engineering and applied mathematics, particularly in fluid mechanics and electromagnetics [1][2][3][4][5]. Nonlinear evolution equations (NLEEs) are foremost in the study of nonlinear phenomena.…”