A New Technique to Achieve Torsional Anchor of Fractional Torsion Equation Using Conservation Laws

Abstract

The main idea in this research is introducing another approximate method to calculate solutions of the fractional Torsion equation, which is one of the applied equations in civil engineering. Since the fractional order is closed to an integer, we convert the fractional Torsion equation to a perturbed ordinary differential equation involving a small parameter epsilon. Then we can find the exact solutions and approximate symmetries for the alternative approximation equation. Also, with help of the definition of conserved vector and the concept of nonlinear self-adjointness, approximate conservation laws(ACL) are obtained without approximate Lagrangians by using their approximate symmetries. In order to apply the presented theory, we apply the Lie symmetry analysis (LSA) and concept of nonlinear self-adjoint Torsion equation, which are very important in mathematics and engineering sciences, especially civil engineering.