Ahmed Bakhet
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View article: Finite Element Method for Time-Fractional Navier–Stokes Equations with Nonlinear Damping
Finite Element Method for Time-Fractional Navier–Stokes Equations with Nonlinear Damping Open
We propose a hybrid numerical framework for solving time-fractional Navier–Stokes equations with nonlinear damping. The method combines the finite difference L1 scheme for time discretization of the Caputo derivative (0<α<1) with mixed fin…
View article: Bicomplex k-Mittag-Leffler Functions with Two Parameters: Theory and Applications to Fractional Kinetic Equations
Bicomplex k-Mittag-Leffler Functions with Two Parameters: Theory and Applications to Fractional Kinetic Equations Open
In this paper, we aim to extend the bicomplex two-parameter Mittag-Leffler (M-L) function by introducing a new k-parameter. This results in the definition of the bicomplex k-M-L function with two parameters. This generalization offers more…
View article: On a new version of bicomplex Mittag-Leffler functions and their applications in fractional kinetic equations
On a new version of bicomplex Mittag-Leffler functions and their applications in fractional kinetic equations Open
The Mittag-Leffler function, often referred to as the ”queen function” of fractional calculus, plays a fundamental role in solving fractional differential equations across various disciplines, including physics and engineering. In this pap…
View article: Some Results of R-Matrix Functions and Their Fractional Calculus
Some Results of R-Matrix Functions and Their Fractional Calculus Open
In this study, we explore various fractional integral properties of R-matrix functions using the Hilfer fractional derivative operator within the framework of fractional calculus. We introduce the θ integral operator and extend its definit…
View article: On the <i>k</i>‐Bicomplex Gamma and <i>k</i>‐Bicomplex Beta Functions and Their Properties
On the <i>k</i>‐Bicomplex Gamma and <i>k</i>‐Bicomplex Beta Functions and Their Properties Open
This paper intends to extend certain special functions from one complex variable to the bicomplex setting. Specifically, we define the k ‐bicomplex Gamma and k ‐bicomplex Beta functions. Subsequently, several properties and formulas pertai…
View article: A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making
A Novel Framework for Belief and Plausibility Measures in Intuitionistic Fuzzy Sets: Belief and Plausibility Distance, Similarity, and TOPSIS for Multicriteria Decision Making Open
Dempster–Shafer Theory (DST) relies significantly on belief and plausibility measures to handle ambiguity and uncertainty; however, DST has been extended to fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs) with only a few extensions f…
View article: Extensions of Bicomplex Hypergeometric Functions and Riemann–Liouville Fractional Calculus in Bicomplex Numbers
Extensions of Bicomplex Hypergeometric Functions and Riemann–Liouville Fractional Calculus in Bicomplex Numbers Open
In this paper, we present novel advancements in the theory of bicomplex hypergeometric functions and their applications. We extend the hypergeometric function to bicomplex parameters, analyse its convergence region, and define its integral…
View article: On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications
On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications Open
In this study, we derive multiple incomplete matrix Mittag-Leffler (ML) functions. We systematically investigate several properties of these incomplete matrix ML functions, which include some general properties and distinct representations…
View article: A Linear Stabilized Incompressible Magnetohydrodynamic Problem with Magnetic Pressure
A Linear Stabilized Incompressible Magnetohydrodynamic Problem with Magnetic Pressure Open
The objective of this article is to examine, stabilize, and linearize the incompressible magnetohydrodynamic model equations. The approximate solutions are carried out through the lowest equal order mixed finite element (FE) approach, invo…
View article: On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties
On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties Open
In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas a…
View article: On the two variables <i>κ</i> -Appell hypergeometric matrix functions
On the two variables <i>κ</i> -Appell hypergeometric matrix functions Open
This work aims to introduce [Formula: see text]-Appell hypergeometric matrix functions [Formula: see text] and [Formula: see text], where [Formula: see text]. New relations for these functions, such as the integral representation, importan…
View article: Investigation of Fractional Calculus for Extended Wright Hypergeometric Matrix Functions
Investigation of Fractional Calculus for Extended Wright Hypergeometric Matrix Functions Open
Throughout this paper, we will present a new extension of the Wright hypergeometric matrix function by employing the extended Pochhammer matrix symbol. First, we present the extended hypergeometric matrix function and express certain integ…
View article: Application of the Pathway-Type Transform to a New Form of a Fractional Kinetic Equation Involving the Generalized Incomplete Wright Hypergeometric Functions
Application of the Pathway-Type Transform to a New Form of a Fractional Kinetic Equation Involving the Generalized Incomplete Wright Hypergeometric Functions Open
We present in this paper a generalization of the fractional kinetic equation using the generalized incomplete Wright hypergeometric function. The pathway-type transform technique is then used to investigate the solutions to a fractional ki…
View article: Incomplete exponential type of $ R $-matrix functions and their properties
Incomplete exponential type of $ R $-matrix functions and their properties Open
In the present paper, we establish the incomplete exponential type (IEF) of $ R $-matrix functions and identify some properties of the incomplete exponential matrix functions including integral representation, some derivative formula and g…
View article: On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus
On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus Open
Through this article, we will discuss a new extension of the incomplete Wright hypergeometric matrix function by using the extended incomplete Pochhammer matrix symbol. First, we give a generalization of the extended incomplete Wright hype…
View article: On the matrix version of extended Struve function and its application on fractional calculus
On the matrix version of extended Struve function and its application on fractional calculus Open
The main goal of this article is to study the extend Struve and extended modified Struve matrix functions by making use of extended Beta matrix function. In particular, we investigate certain important properties of these extended matrix f…
View article: Matrix-Valued hypergeometric Appell-Type polynomials
Matrix-Valued hypergeometric Appell-Type polynomials Open
In recent years, much attention has been paid to the role of special matrix polynomials of a real or complex variable in mathematical physics, especially in boundary value problems. In this article, we define a new type of matrix-valued po…
View article: On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions
On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions Open
In this paper, we first introduce the incomplete extended Gamma and Beta functions with matrix parameters; then, we establish some different properties for these new extensions. Furthermore, we give a specific application for the incomplet…
View article: Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions
Degenerate Analogues of Euler Zeta, Digamma, and Polygamma Functions Open
In recent years, much attention has been paid to the role of degenerate versions of special functions and polynomials in mathematical physics and engineering. In the present paper, we introduce a degenerate Euler zeta function, a degenerat…
View article: On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial
On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial Open
In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended…
View article: On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals
On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals Open
In this paper, we first introduce the 2-variables Konhauser matrix polynomials; then, we investigate some properties of these matrix polynomials such as generating matrix relations, integral representations, and finite sum formulae. Finall…
View article: Two Variables Shivley’s Matrix Polynomials
Two Variables Shivley’s Matrix Polynomials Open
The principal object of this paper is to introduce two variable Shivley’s matrix polynomials and derive their special properties. Generating matrix functions, matrix recurrence relations, summation formula and operational representations f…