Fractional (3+1)-dim Jimbo Miwa system: invariance properties, exact solutions, solitary pattern solutions and conservation laws

Abstract

The present article is devoted to scouting invariant analysis and some kind of approximate and explicit solutions of the (3+1)-dimensional Jimbo Miwa system of nonlinear fractional partial differential equations (NLFPDEs). Feasible vector field of the system is obtained by employing the invariance attribute of one-parameter Lie group of transformation. The reduction of the number of independent variables by this method gives the reduction of Jimbo Miwa system of NLFPDES into a system of nonlinear fractional ordinary differential equations (NLFODEs). Explicit solutions in form of power series are scrutinized by using power series method (PSM). In addition, convergence is also examined. The residual power series method (RPSM) is employed for disquisition of solitary pattern (SP) solutions in form of approximate series. A comparative analysis of the obtained results of the considered problem is provided. The conserved vectors are scrutinized in the form of fractional Noether’s operator. Numerical solutions are represented graphically.

Space time fractional Ito system with variable coefficients: explicit solution, conservation laws and numerical approximation

“…Researchers have recently become concerned in fractional differential equations (FDEs). FDEs have been analyzed by plenty of academics in order to obtain exact answers employing various methodologies (Akbulut and Kaplan, 2018;Jia and Wang, 2018;Chen and Jiang, 2018;H€ o€ ok et al, 2018;Osman et al, 2019;Abdel-Gawad and Osman, 2013;Zhang, 2017;Kiryakova, 1994;Podlubny, 1999;Samko et al, 1993;Senol et al, 2019;Senol, 2020;Kumar, 2019a, 2019b;Kumar and Kour, 2020). Nonlinear equations corresponding to a specific category in terms of symmetrical groups must be classified in modern Lie group analysis.…”

“…, 2019; Senol, 2020; Kour and Kumar, 2019a, 2019b; Kumar et al. , 2021; Kumar and Kour, 2020). Nonlinear equations corresponding to a specific category in terms of symmetrical groups must be classified in modern Lie group analysis.…”