Document Type : Research Paper

**Authors**

Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.

**Abstract**

In this work, we use the symmetry of the Lie group analysis as one of the powerful tools that deals with the wide class of fractional order differential equation in the Riemann-Liouville concept. We employ the classical Lie symmetries to obtain similarity reductions of nonlinear time-fractional Benjamin-Ono equation and then, we find the related exact solutions for the derived generators. Finally, according to the Lie symmetry generators obtained, we construct conservation laws for related classical vector fields of time-fractional Benjamin-Ono equation.

**Keywords**

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July 2022

Pages 608-616

**Receive Date:**14 April 2021**Revise Date:**24 July 2021**Accept Date:**30 July 2021**First Publish Date:**08 August 2021