Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable

• Main Authors: Najla M. Alarifi, Rabha W. Ibrahim
• Format: Article
• Language: English
• Published: Hindawi Limited 2021-01-01
• Series: Journal of Function Spaces
• Online Access: http://dx.doi.org/10.1155/2021/4797955

Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope.