Ali Youssef

Ali Youssef
Sohag University · Department of Mathematics

MS
Complex Analysis & Fractional Calculus & Special Functions & Hyper-Complex Analysis & Mathematical Physics

About

8
Publications
932
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8
Citations
Introduction
Ali.M. Youssef currently works at the math, Sohag University. Ali is interested in the field of complex analysis especially, Higher transcendental functions in fractional setting, Higher transcendental functions in Matrix context and Higher transcendental functions in Hyper-Complex foreword.
Additional affiliations
December 2016 - present
Sohag University
Position
  • Sohag
Education
December 2016 - August 2020
Sohag University
Field of study
  • Pure Mathematics- Mathematical Analysis

Publications

Publications (8)
Thesis
The higher transcendental functions (special functions) have an increasing and recognized role in mathematical physics, fractional calculus, theory of differential equations, quantum mechanics, approximation theory and many branches in science. Special functions have a long history that can be traced back to the past three centuries where the probl...
Data
International Symposium on “Recent Advances in Fractional Calculus” organized by Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences (PDPIAS), Charotar University of Science and Technology (CHARUSAT), Changa (388 421), Gujarat, India held on 30th September and 1st October, 2021.
Article
Full-text available
The theory of Bessel functions is a rich subject due to its essential role in providing solutions for differential equations associated with many applications. As fractional calculus has become an efficient and successful tool for analyzing various mathematical and physical problems, the so-called fractional Bessel functions were introduced and stu...
Article
Full-text available
This article presents an exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric differential equation (CFGHDE) about the fractional regular singular points x=1 and x=∞. Next, various generating functions of the CFGHF are established. We also develop s...
Article
Full-text available
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the conformable fractional differentiation. We introduce the CFLPs via different generating functions and provide som...
Preprint
Full-text available
This paper presents a somewhat exhaustive study on the conformable fractional Gauss hypergeometric function (CFGHF). We start by solving the conformable fractional Gauss hypergeometric equation (CFGHE) about the fractional regular singular points $x=1$ and $x=\infty$. Next, various generating functions of the CFGHF are established. We also develop...
Preprint
Full-text available
The main objective of this paper is to give a wide study on the conformable fractional Legendre polynomials (CFLPs). This study is assumed to be a generalization and refinement, in an easy way, of the scalar case into the context of the conformable fractional differentiation. We introduce the CFLPs via different generating functions and provide som...

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Projects

Projects (2)
Project
The diversity of problems about the theory of partial differential equations, which we wish to study requires a number of distinct methods from potential theory, mathematical physics, discrete function theory, differential geometry, etc. Thus even though the individual parts of the research are intimately connected, most of the goals are methodically largely independent of each other.
Project
The higher transcendental functions (special functions) have an increasing and recognised role in mathematical physics, fractional calculus, theory of differential equations, quantum mechanics, approximation theory and many branches in science. Special functions have a long history that can be traced back to the past three centuries where the problems of terrestrial and celestial mechanics that were solved in the eighteenth and nineteenth centuries, the boundary value problems of electromagnetism and heat in the nineteenth and the eigenvalue problems of quantum mechanics in the twentieth. The study of higher transcendental functions (special functions) grew up with the calculus and is consequently one of the oldest branches of analysis. The discoveries of new special functions and their applications to new areas of mathematics have initiated a resurgence of interest in this field. Much attention has been devoted over the past decades to generalizing the Theory of Special Functions within two fundamental directions: a fractional calculus and a higher-dimensional setting, mainly motivated by the problems coming from the fields ranging from applied mathematics to classical problems of physics and engineering. Accordingly, the main goal of this work is studying some new interesting higher transcendental functions, investigating some important convergence properties of the in the sense of fractional calculus, and hence provide with some methods to solve different kind of fractional differential equations which are much close to some interesting applications.