**Numerical Investigation of Multiple Solutions for Caputo Fractional-Order-Two Dimensional Magnetohydrodynamic Unsteady Flow of Generalized Viscous Fluid over a Shrinking Sheet Using the Adams-Type Predictor-Corrector Method**

**Liaquat Ali Lund 1,2, Zurni Omar 1, Sayer O. Alharbi 3, Ilyas Khan 4,\* and Kottakkaran Sooppy Nisar <sup>5</sup>**


Received: 29 April 2019; Accepted: 13 June 2019; Published: 27 August 2019

**Abstract:** In this paper, magnetohydrodynamic (MHD) flow over a shrinking sheet and heat transfer with viscous dissipation has been studied. The governing equations of the considered problem are transformed into ordinary differential equations using similarity transformation. The resultant equations are converted into a system of fractional differential boundary layer equations by employing a Caputo derivative which is then solved numerically using the Adams-type predictor-corrector method (APCM). The results show the existence of two ranges of solutions, namely, dual solutions and no solution. Moreover, the results indicate that dual solutions exist for a certain range of specific parameters which are in line with the results of some previously published work. It is also observed that the velocity boundary layer decreases as the suction and magnetic parameters increase.

**Keywords:** APCM; Caputo derivative; dual solutions; unsteady flow; MHD; shrinking surface
