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.

中文翻译：

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分数 (3+1)-dim Jimbo Miwa 系统：不变性、精确解、孤立模式解和守恒定律

摘要 本文致力于探索非线性分数阶偏微分方程 (NLFPDE) 的 (3+1) 维 Jimbo Miwa 系统的不变量分析和某种近似和显式解。利用变换的单参数李群的不变性属性得到系统的可行向量场。通过这种方法减少自变量的数量，将 NLFPDES 的 Jimbo Miwa 系统简化为非线性分数阶常微分方程 (NLFODE) 系统。使用幂级数方法 (PSM) 仔细检查幂级数形式的显式解。此外，还检查了收敛性。残差幂级数法 (RPSM) 用于以近似级数的形式研究孤立模式 (SP) 解。对所考虑问题的所得结果进行了比较分析。以分数 Noether 算子的形式仔细检查守恒向量。数值解以图形表示。