Atangana-Baleanu and Caputo Fabrizio Analysis of Fractional Derivatives for Heat and Mass Transfer of Second Grade Fluids over a Vertical Plate: A Comparative Study

作者：Khan Arshad; Abro Kashif Ali; Tassaddiq Asifa; Khan Ilyas^*

来源：Entropy, 2017, 19(8): 279.

DOI：10.3390/e19080279

• AB and CF derivatives
• M-function M-q(p)(z) and generalized Hyper-geometric p)Psi(q)(z)
• convection flow
• heat and mass transfer
• exact solutions

This communication addresses a comparison of newly presented non-integer order derivatives with and without singular kernel, namely Michele Caputo-Mauro Fabrizio (CF) (CF)(partial derivative(beta)/partial derivative t(beta)) and Atangana-Baleanu (AB) (AB) (partial derivative(alpha)/partial derivative t(alpha)) fractional derivatives. For this purpose, second grade fluids flow with combined gradients of mass concentration and temperature distribution over a vertical flat plate is considered. The problem is first written in non-dimensional form and then based on AB and CF fractional derivatives, it is developed in fractional form, and then using the Laplace transform technique, exact solutions are established for both cases of AB and CF derivatives. They are then expressed in terms of newly defined M-function M-q(p)(z) and generalized Hyper-geometric p)Psi(q)(z). The obtained exact solutions are plotted graphically for several pertinent parameters and an interesting comparison is made between AB and CF derivatives results with various similarities and differences.

• 出版日期2017-8