Lie Symmetry Analysis and Conservation Laws  for the Time Fractional Biased Random Motion Equation

Brahim El Ansari; El hassan El kinani; Abdelaziz Ouhadan

doi:10.5269/bspm.69185

Lie Symmetry Analysis and Conservation Laws for the Time Fractional Biased Random Motion Equation

Brahim El Ansari Laboratory of Mathematics, Analysis and Control of Systems, Department of Mathematics, Faculty of Sciences, Moulay Ismail University https://orcid.org/0000-0002-8148-171X
El hassan El kinani Laboratory of Mathematics, Analysis and Control of Systems, Department of Mathematics https://orcid.org/0009-0007-1748-1209
Abdelaziz Ouhadan Laboratory of Mathematics, Analysis and Control of Systems, Department of Mathematics https://orcid.org/0000-0002-3968-8143

Résumé

In this paper, the Lie group method is applied. The group generators are obtained for the time fractional Biased random motion equation. They are employed to reduce the studied fractional equation with Riemann-Liouville fractional time derivatives to a family of fractional ordinary differential equations and in some particular cases with Erd\'elyi-Kober fractional operator. Moreover, some exact solutions and conserved quantities are given.