Fractional Boundary Layer Flow and Heat Transfer Over a Stretching Sheet With Variable Thickness

The paper gives a comprehensive study on the space fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness, and the variable magnetic field is applied. Novel governing equations with left and right Riemann-Liouville fractional derivatives subject to irregular region are formulated. By introducing new variables, the boundary conditions change as the traditional ones. Solutions of the governing equations are obtained numerically where the shifted Grunwald formulae are applied. Good agreement is obtained between the numerical solutions and exact solutions which are constructed by introducing new source items. Dynamic characteristics with the effects of involved parameters on the velocity and temperature distributions are shown and discussed by graphical illustrations. Results show that the velocity boundary layer is thicker for a larger fractional parameter or a smaller magnetic parameter, while the temperature boundary layer is thicker for a larger fractional parameter, a smaller exponent parameter, or a larger magnetic parameter. Moreover, it is thicker at a smaller y and thinner at a larger y for the velocity boundary layer with a larger exponent parameter while for the velocity and temperature boundary layers with a smaller weight coefficient.