Chaos, Solitons and Fractals 140 (2020) 110161 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos Analysis of MHD generalized first problem of Stokes’ in view of local and non-local fractal fractional differential operators Imran Siddique a , Ali Akgül b,∗ a Department of Mathematics, University of Management and Technology Lahore, Pakistan b Siirt University Art and Science Faculty Department of Mathematics, Siirt TR-56100, Turkey a r t i c l e i n f o Article history: Received 20 June 2020 Revised 16 July 2020 Accepted 25 July 2020 Keywords: Fractal fractional derivative Mittag-Leffler kernel Stability analysis Discretization a b s t r a c t In this work, we investigate the unsteady MHD generalized first problem of Stokes’ for an incompress- ible viscous fluid under isothermal conditions. The developed governing equations for the problem are formulated with the newly introduced fractal fractional operators with power law, exponential decay law and the Mittag-Leffler law kernels. For every operator, we give a point by point examination including, numerical arrangement and stability investigation. Likewise, we present some numerical recreation. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction Viscous fluid flow between parallel plates has been broadly concentrated because of its extensive implementations in various parts of sciences and engineering. Couette flow has many imple- mentations in aerodynamics heating, polymer innovation, oil pro- duction and cleaning of unrefined petroleum, water driven lifts and numerous factual handling applications [1]. This sort of issue has a lot of significance [2]. Magnetohydrodynamics (MHD) is a physical numerical struc- ture that worries the elements of attractive fields electrically lead- ing liquids e.g., in plasma and fluid metals. The MHD flows of New- tonian fluid between two equal plates have been one of the sub- jects which stood out of numerous analysts because of their me- chanical and innovative applications. Such flows have significant claims in polymer manufacturing and metallurgy where hydromag- netic strategies are being utilized. In astronomy and geophysics, MHD is applied to the investigation of cosmological and sunlight based assemblies, interstellar issue, radio spread through the iono- sphere, etc. Soundalgekar et al. [3,4] and Raptis and Singh [5] ap- pear to be the primary creators who contemplated the impact of magnetic field in their works. Likewise, numerous analysts have contributed in examining MHD and heat transfer in permeable and non-permeable media. The impact of the transversely applied mag- netic field on convection flows of an electrically conducting fluid has been researched; see [6–10] and references in that. ∗ Corresponding author. E-mail address: aliakgul00727@gmail.com (A. Akgül). In most recent couple of decades, fractional calculus has gotten a quick fame in numerous spaces and become an appealing sub- ject for mathematicians. At present, fractional dynamical equations perform a significant act in the displaying of unusual conduct and reminiscence impacts that are basic attributes of regular marvels [11]. An emerging piece of studies in academic control and engi- neering science take into consideration the dynamic system dis- played by the set of equations of non-integer order that necessitate derivatives and integrals of non-integer order [2]. These recently evolved replicas are typically significantly more sufficient than pre- viously implemented integer order structures. As fractional order differentials and integrals represent the memory and complex in- gredients analyzed by Zaslavsky [12] and Poddulony [13]. These are the for all intents and purposes critical favorable position of non- integer order in comparing with integer order, in which such im- pacts are ignored. Utilizations of fractional derivative replicas may be found in the systems of polymers in the glass state, wire and fiber cov- ering, chemically prepared supplies, in the structuring of a few heat motors or heat exchangers. Numerous analysts has adjusted the old style fluid models to fractional models by supplanting the traditional, time-derivatives of an integer order, by the so called Riemann-Liouville (RL), Caputo, Caputo-Fabrizio (CF) and Atangana- Baleanu (AB) differential integral operators [14–17]. Imran et al. [18] recently implemented the CF and AB derivatives to the is- sue planned because of transfer of heat in second grade viscoelas- tic fluid. Imran and Mehwish [19] implemented the CF differen- tials and inspected convective progression of a generalized second grade fluid system. Imran et al. [20] created heat transfer issues by https://doi.org/10.1016/j.chaos.2020.110161 0960-0779/© 2020 Elsevier Ltd. All rights reserved.