Eur. Phys. J. Plus (2019) 134: 417
https://doi.org/10.1140/epjp/i2019-12808-6

Regular Article

Invariant subspace and approximate analytic solutions of a fractional model of convective longitudinal fins in thermal conductivity

¹ Department of Mathematics, Sun Yat-Sen University, Guangzhou, China
² Department of Mathematics, Faculty of Science, Federal University Dutse, Jigawa, Nigeria
³ Department of Mathematics, King Saud University, 11495, Riyadh, Saudi Arabia

^* e-mail: aliyu@mail.sysu.edu.cn

Received: 9 January 2019
Accepted: 10 June 2019
Published online: 2 September 2019

Abstract

In this work, a fractional model of convective longitudinal fins in thermal conductivity are studied by using the invariant subspace method (ISM). The method determines an invariant subspace and construct the exact solutions of the partial differential equations (PDEs) by reducing them to ordinary differential equations (ODEs). As a result of the calculations, exponential solutions of the model are derived. Furthermore, the two step Adomian decomposition method (TSADM) and the Padé approximation techniques are used to derive the Padé approximate solutions of the model. The are derived along with interesting figures showing both the exact and approximate solutions. Ultimately, for illustrating the acquired results, some numerical simulations are performed.