Application of the modern trend of fractional differentiation to the MHD flow of a generalized Casson fluid in a microchannel: Modelling and solution<sup>⋆</sup>

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European Physical Journal Plus, 2018, 133 (7)
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© 2018, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature. The motivation for writing this article is based on the contributions of Atangana and Baleanu to the fractal and fractional differentiation. Recently, Atangana and Baleanu launched a new fractional operator, namely, the Atangana-Baleanu fractional operator with the Mettang-Leffler function as the kernel of integration. This new operator is an efficient tool to model complex and real-world problems. This article deals with modeling and solution of the generalized magnetohydrodynamic (MHD) flow of a Casson fluid in a microchannel. This microchannel is taken of infinite length in the vertical direction and of finite width in the horizontal direction. The flow is modeled in terms of a set of partial differential equations involving the Atnagana-Baleanu time fractional operator along with physical initial and boundary conditions. The partial differential equations are transformed to ordinary differential equations via the fractional Laplace transformation and are solved for an exact solution using the transformed conditions. To explore the physical significance of various pertinent parameters affecting the flow, the numerical techniques of Zakian and Tzou are utilized for inversion of the Laplace transformation. The results obtained here may have useful industrial and engineering applications.
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