Abstract
The impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established in terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transforms. The change in the momentum profile due to variability in the values of parameters is graphically illustrated for all three C, CF and ABC models. The ABC model has proficiently revealed a memory effect.
Highlights
Over the past thirty years, fractional derivatives have fascinated multiple researchers as compared to classical derivatives
Fractional derivatives and Laplace transforms are applied to examine the solutions for nondimensional fractional models
Several graphs are presented to illustrate the physical effects of parameters γ, λ, Schmidt number (Sc), Prandtl number (Pr), Thermal Grashof number (Gr), Mass Grashof number (Gm) and M on velocity
Summary
Over the past thirty years, fractional derivatives have fascinated multiple researchers as compared to classical derivatives. Where m1 = q + M, p = λ(q + M) – Pr and s = λ(q + M) – Sc. 6.3 Caputo–Fabrizio fractional derivative Theorem 3 Let CF Dγt i(ζ , t) be the Caputo–Fabrizio fractional derivative and L be the Laplace operator, applying these operators to Eq (4) along with initial and boundary conditions, the exact solution of velocity is given in Eq (33). Where m1 = q + M, l = 1 – γ , d = 1 – γ + λ, p2 = m1d – Pr and s2 = m1d – Sc. 6.4 Atangana–Baleanu fractional derivative Theorem 4 Let ABCDγt i(ζ , t) be the Atangana–Baleanu fractional derivative and L be the Laplace operator, applying these operators to Eq (4) along with initial and boundary conditions, the exact solution of velocity is given in Eq (40). 7.3 Case 3 By eliminating the concentration and magnetic field simultaneously we obtain the results shown in Raza and Asad Ullah [23]
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