This research paper uses a direct algebraic computational scheme to construct the Jacobi elliptic solutions based on the conformal fractional derivatives for nonlinear partial fractional differential equations (NPFDEs). Three vital models in mathematical physics [the space-time fractional coupled Hirota Satsuma KdV equations, the space-time fractional symmetric regularized long wave (SRLW equation), and the space-time fractional coupled Sakharov–Kuznetsov (S–K) equations] are investigated through the direct algebraic method for more explanation of their novel characterizes. This approach is an easy and powerful way to find elliptical Jacobi solutions to NPFDEs. The hyperbolic function solutions and trigonometric functions where the modulus and, respectively, are degenerated by Jacobi elliptic solutions. In this style, we get many different kinds of traveling wave solutions such as rational wave traveling solutions, periodic, soliton solutions, and Jacobi elliptic solutions to nonlinear evolution equations in mathematical physics. With the suggested method, we were fit to find much explicit wave solutions of nonlinear integral differential equations next converting them into a differential equation. We do the 3D and 2D figures to define the kinds of outcome solutions. This style is moving, reliable, powerful, and easy for solving more difficult nonlinear physics mathematically.

中文翻译：

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求解数学物理学中分数阶的三个非线性生命模型的代数计算方法

本文采用直接代数计算方案，基于非线性分数阶微分方程（NPFDEs）的共形分数导数构造Jacobi椭圆解。数学物理学中的三个重要模型[时空分数耦合的Hirota Satsuma KdV方程，时空分数对称的正则长波（SRLW方程）和时空分数耦合的Sakharov–Kuznetsov（S–K）方程]是通过直接代数方法进行调查，以进一步解释其新颖性。这种方法是找到NPFDE椭圆Jacobi解决方案的简便而有效的方法。双曲函数解和三角函数，其中模和分别由雅可比椭圆解退化。用这种风格 我们得到了许多不同种类的行波解，例如数学物理中非线性发展方程的有理波行解，周期解，孤子解和Jacobi椭圆解。使用建议的方法，我们适合找到非线性积分微分方程的显式波解，然后将其转换为微分方程。我们使用3D和2D图形来定义结果解决方案的种类。这种风格是移动的，可靠的，强大的，并且易于用数学方法解决更困难的非线性物理。我们适合找到非线性积分微分方程的显式波动解，然后将其转换为微分方程。我们使用3D和2D图形来定义结果解决方案的种类。这种风格是移动的，可靠的，强大的，并且易于用数学方法解决更困难的非线性物理。我们适合找到非线性积分微分方程的显式波动解，然后将其转换为微分方程。我们使用3D和2D图形来定义结果解决方案的种类。这种风格是移动的，可靠的，强大的，并且易于用数学方法解决更困难的非线性物理。