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

Najla M Alarifi,Rabha W Ibrahim,Badr Saad T Alkaltani

doi:10.1155/2021/4797955

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.

Highlights

Fractional calculus has expanded considerable attention primarily appreciations to the growing occurrence of investigation mechanisms in the life sciences, allowing for simulations found by fractional operators [1] including differential and integral formulas
The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions, and other studies are illustrated in the sequel
We investigate the upper bound of the 2dimensional Saint-Venant equations (2D-SVE) of diffusive wave

Summary

Introduction

Fractional calculus has expanded considerable attention primarily appreciations to the growing occurrence of investigation mechanisms in the life sciences, allowing for simulations found by fractional operators [1] including differential and integral formulas. The mathematical investigation of fractional calculus has advanced, chief to connections with other mathematical areas such as probability theory, mathematical physics [2], and mathematical biology [3,4,5,6,7] and the investigation of stochastic processes in real cases. It appears in studies of complex analysis. Some definitions such as the Hilfer and Prabhakar results [12] (differential and integral operators) are essentially the theme of mathematical study

Objectives

Conclusion