Symmetry results for solutions of equations involving zero-order operators

Second order symmetry operators

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed ...

Subordination and Super Ordination Results Involving Certain Convolution Operators

Application of the Lie Symmetry Analysis for second-order fractional differential equations

Obtaining analytical or numerical solution of fractional differential equations is one of the troublesome and challenging issue among mathematicians and engineers, specifically in recent years. The purpose of this paper Lie Symmetry method is developed to solve second-order fractional differential equations, based on conformable fractional derivative. Some numerical examples are presented to il...

λ-Symmetry method and the Prelle-Singer method for third-order differential equations

In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...

Lie symmetry analysis for Kawahara-KdV equations

We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.