In this research, the analytical and numerical solutions of the fractional nonlinear space-time Phi-four model are investigated by employing two systematic schemes and the B-spline schemes. A new fractional operator definition is applied to this model to convert the model from its fractional formula to an integer-order nonlinear ordinary differential equation. The considered model is of major interest for studying the nuclear interaction, elementary particles in a condensed medium, and propagation of dislocations in crystals. Explicit wave solutions are obtained.

中文翻译：

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分数非线性时空核模型的新显解

本研究采用两种系统格式和B样条格式研究分数非线性时空Phi-4模型的解析解和数值解。新的分数算子定义应用于该模型，将模型从分数公式转换为整数阶非线性常微分方程。所考虑的模型对于研究核相互作用、凝聚介质中的基本粒子和晶体中位错的传播具有重要意义。获得显式波解。