**Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface**

**Liaquat Ali Lund 1,2 , Zurni Omar <sup>1</sup> , Ilyas Khan 3,\*, Dumitru Baleanu 4,5,6 and Kottakkaran Sooppy Nisar <sup>7</sup>**


Received: 11 March 2020; Accepted: 27 March 2020; Published: 9 April 2020

**Abstract:** In this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.

**Keywords:** similarity solution; triple solutions; stability analysis; shooting method; three-stage Lobatto III-A formula
