Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable. (10th September 2021)

• Record Type: Journal Article
• Authors: Alarifi, Najla M.; Ibrahim, Rabha W.
• Other Names: Saad. T. Alkaltani Badr Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-09-10
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/4797955
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.