HAMZA Mihoubi

Mariam, NOUIOUA

Analytical solutions for Navier-Stokes Equations with Caputo Fractional Derivative

Hadji abedelaziz

Hpltm for Numerical simulation of multi dimensionl, time fractional model of Navire Stokes équation

DJAIDJA RAWIYA

Simulation numérique de transfert thermique en utilisant les coordonnées curvilignes

ZAOUCHE Meftah

Simulation numérique d’un écoulement autour d’un obstacle

Using the Homotopy Perturbation Laplace Transform Method (HPLTM), the objective of our current work is to find the analytical solution of the nonlinear fractional partial differential equations arising in the spatial diffusion model of biological populations. This is achieved by replacing the Caputo fractional derivative of the Riemann-Liouville model with the Catogambola fractional derivative represented in the Caputo type. Moreover, the homotopy perturbation transform technique integrates the Laplace transform with the homotopy perturbation method. In addition, the efficiency of the proposed method is verified through three test examples. Accordingly, the results obtained by applying the proposed method for different fractional orders are plotted, and a comparative analysis is performed between our results and those of previous studies.

Citation

Hamza Mihoubi , , (2025-12-31), Solving Time-Fractional Nonlinear Partial Differential Equations that Arise in the Biological Populations’ Spatial Diffusion Under Caputo-Katugampola Memory, Mathematical Modelling of Engineering Problems, Vol:12, Issue:12, pages:14, International Information and Engineering Technology Association

In the present study, we aimed to derive analytical solutions of the homotopy analysis method (HAM) for the time-fractional Navier–Stokes equations in cylindrical coordinates in the form of a rapidly convergent series. In this work, we explore the time-fractional Navier–Stokes equations by replacing the standard time derivative with the Katugampola fractional derivative, expressed in the Caputo form. The homotopy analysis method is then employed to obtain an analytical solution for this time-fractional problem. The convergence of the proposed method to the solution is demonstrated. To validate the method’s accuracy and effectiveness, two examples of time-fractional Navier–Stokes equations modeling fluid flow in a pipe are presented. A comparison with existing results from previous studies is also provided. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations applied in engineering mathematics.

Citation

Hamza Mihoubi , , (2025-11-02), Solution of Fraction Navier–Stokes Equation Using Homotopy Analysis Method, AppliedMath, Vol:5, Issue:148, pages:19, Multidisciplinary Digital Publishing Institute (MDPI)

The aim of the paper is to present a numerical technique that applies the homotopy perturbation method to solve the time-Fractional Black-Scholes European option pricing equation with boundary conditions. The study employs the 𝜑 − Caputo Fractional derivative in time, and the operator admits as particular cases the Caputo and Caputo–Hadamard Fractional derivatives describe the solutions of these equations that contribute to the generalization and development of certain recent results. The method offers a convergent series with easily computed components as an analytical solution. The method outperforms currently available analytical techniques without the need for linearization or minor perturbations. The homotopy perturbation approach is a practical and efficient way to get over the limitations of more conventional techniques, as demonstrated by the two examples presented under Caputo–Hadamard memory, when applied to the time-Fractional Black-Scholes European option pricing equation, the techniques' accuracy and ease of implementation are demonstrated by the numerical findings.

Citation

Hamza Mihoubi , , (2025-05-31), Analytical Solutions for Fractional Black-Scholes European Option Pricing Equation by Using Homotopy Perturbation Method with Caputo Fractional Derivative, Mathematical Modelling of Engineering Problems, Vol:12, Issue:5, pages:1562-1570, International Information and Engineering Technology Association

In this study, we tackle the time fractional discrete Navier-Stokes equation by employing the homotopyperturbation ρ-Laplace transform method (HPLTM), utilizing the Caputo-Katugampola fractional derivative of time.Additionally, we present graphical representations of the solution generated using Matlab software, comparing it withthe exact solution for α = 1. We perform two test problems to verify and demonstrate the effectiveness of our approach.Our numerical findings and graphical analyses indicate that the proposed approach exhibits remarkable efficiency andsimplicity, rendering it suitable for addressing a diverse array of challenges encountered in engineering and the sciences

Citation

YACINE Arioua , Hamza Mihoubi , BRAHIM Bouderah , Awatif Alghahtani, , (2025-03-18), Homotopy Perturbation ρ-Laplace Transform Approach for Numerical Simulation of Fractional Navier-Stokes Equations, Contemporary Mathematics, Vol:6, Issue:3, pages:1-33, Universal Wiser Publisher

The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace transform (LT). The time-fractional derivative used is the Caputo–Hadamard fractional derivative (CHFD). The effectiveness of this method is demonstrated and validated through two test problems. The results show that the proposed method is robust, efficient, and easy to implement for both linear and nonlinear problems in science and engineering. Additionally, its computational efficiency requires less computation compared to other schemes.

Citation

Hamza Mihoubi , , (2024-12-31), Analytical Solutions of Time-Fractional Navier-Stokes Equations Employing Homotopy Perturbation-Laplace Transform Method, Fractal and Fractional, Vol:9, Issue:1, pages:21, Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/).

We introduce an analytical method, namely the Homotopy perturbation Laplace transforms method (HPLTM), which is a combination of the Homotopy perturbation Laplace transforms method (HPLTM). Anew application of the HPLTM is presented for the solution of the fractional order fractional Navier – Stokes equation. The accuracy and efficiency of the proposed method is verified through with exact solutions extracted. However, the plan has proven to be a very dependable, strong and efficient method for resolving a variety of issues in the sciences and engineering. Besides, its strength is that it requires less calculation in contrast to the other techniques. It will be covered in more detail in future applied work in the fields of fluid mechanics.

Citation

Hamza Mihoubi , ,(2024-05-15), Analytical solution of time-fractional Navier–Stokes equation by use of HPLTM,International Conference on Nonlinear Mathematical Analysis and Its Applications (IC-NMAA’24).,BORDJ BOU ARRÉRIDJ – ALGERIA

Abstract In this paper, the enhancement of heat transfer in horizontal rings was investigated using nanofluids Where a nanofluids of a different basic nature was used, which is composed of glycerine, motor oil and ethylene glycol (EG). It contains different volume fractions of Ag nanoparticles. For the inner and outer cylinder they were used at temperatures Tc and Tf, respectively with Tc > Tf. For solving the equations numerically, (continuity, momentum, and energy) the finite volume method (MVF) was used. The Maxwell-Garnett (MG model) equation is used to determine the effective thermal conductivity and viscosity of the nanofluid mixture and Brinkman models, respectively results were presented in terms of isotherms, fluid flow models, the Rayleigh numbers Nusselt distribution function, and the volume fraction of silver nanoparticles. The obtained results are discussed in detail. It can be said that the results of this study are fully consistent with previous theoretical studies.

Citation

Hamza Mihoubi , ,(2023-11-26), Numerical Study of Natural Convection in Horizontal Centrality annuli using Nanofluid,International Conference on Contemporary Mathematics and its Applications (ICCMA 2023),University Center Abdelhafid Boussouf of Mila, Algeria

Ce contenu présente MATLAB applications différentes en mathématiques appliquées et en mécanique. L’objectif est de travailler sur l’utilisation de méthodes numériques dans des exemples qui soulignent l’importance de MATLAB comme outil de programmation efficace. MATLAB offre un accès facile à divers algorithmes élémentaires et avancés pour le calcul numérique. Ces algorithmes comprennent des opérations sur l'algèbre matricielle, la recherche de solutions aux équations différentielles, les statistiques de base, la synthèse et l'analyse de données linéaires et la réduction de données. De nombreuses fonctions de base de MATLAB sont utilisées avec certaines des fonctions développées par les auteurs. Fortran est le langage de programmation préféré pour résoudre de nombreux problèmes de sport et d'ingénierie sur les ordinateurs numériques. Après cela, le programme MATLAB, qui facilite le développement du programme, est apparu avec d'excellents diagnostics d'erreur et les capacités des instructions de programmation. De sorte que les matrices sont traitées avec une grande efficacité avec de nombreuses fonctions qui effectuent une algèbre linéaire. Permettez une préparation facile des graphiques de qualité de publication et des tracés de surface pour les articles techniques et les livres. Les auteurs ont constaté que les programmes MATLAB sont souvent significativement plus courts que les versions FORTRAN correspondantes. Par conséquent, plus de temps est Disponible dans le but principal de l'informatique, à savoir mieux comprendre le comportement du système physique. Les programmes MATLAB ont été écrits principalement pour servir d’exemples éducatifs dans la recherche avancée en mathématiques d’ingénierie et les méthodes numériques appliquées. Le plus grand avantage pour le lecteur est susceptible d’être tiré de l’étude des programmes principalement liés aux applications de physique et d’ingénierie. MATLAB travaille maintenant dans de nombreuses universités à travers le monde et dans de nombreuses communautés d’utilisateurs à travers le monde. Le développement continu sera amélioré en travaillant à réduire les coûts des dispositifs de programmation afin de familiariser davantage de personnes avec les méthodes avancées de programmation.

Citation

HamzaMihoubi , ,(2023-01-09); Travaux pratiques de programmation en MATLAB,Université de Mohamed Boudiaf -M’sila-,

This document is an introduction to MATLAB, scientific computing software. Its objective is to prepare the student for practical work in Automatic Control, Mechanics and Numerical Analysis in which this tool is intensively used for the application and simulation of the theoretical principles presented in class. In addition, this manual offers the opportunity for the student to train in widely used professional software. Cleve Moler, then a professor of computer science at the University of New Mexico, created MATLAB in the 1970s to help his students. It was engineer Jack little who identified the commercial potential of MATLAB in 1983. C. Moler, J. little, and Steve Bangart created MathWorks in 1984 and rewrote MATLAB in C. MATLAB allows interactive work either in command mode or in programming mode; While still having the possibility of making graphic visualizations. Considered one of the best programming languages (C or FORTRAN), MATLAB has the particularities following with respect to these languages:  Easy programming,  Continuity among integer, real and complex values,  The wide range of numbers and their precision,  The very comprehensive mathematical library,  The graphical tool which includes graphical interface functions and utilities,  The possibility of linking with other classic programming languages (C or FORTRAN). The best way to learn how to use this software is to use it yourself, by experimenting, making mistakes and trying to understand the error messages that will be returned to you. These messages are in English! This document is intended to help you for some first steps with MATLAB.

Citation

HamzaMihoubi , ,(2022-01-09); Polycopied course for the module Programming Tools 2 with MATLAB,Université de Mohamed Boudiaf -M’sila-,

A numerical study based on the analysis of laminar natural convection in a concentric cylindrical annulus heat exchanger is investigated. The operating fluid is confined between two horizontal concentric cylinders which are maintained at different uniform temperatures. The governing equations the flow (of continuity, momentum and energy) are numerically solved via finite volume method (FVM). The investigation is performed for Rayleigh number and volume fraction of nanoparticles in the range of 103 -105 and 0-12%, respectively. The effective thermal conductivity and viscosity of the nanofluids mixture are calculated via Maxwell-Garnett model (MG-model) and Brinkman model, respectively. The results are presented in terms of isotherms, fluid flow patterns and Nusselt number distribution function of Rayleigh number and the volume fraction of silver nanoparticles. The results are also discussed in detail. Results are discussed in detail. It is found that a very good agreement exists between the present results and those from the literature. It is found that fluid flow intensity and heat transfer rate increase with the increase of the nanoparticles volume fraction and Rayleigh number, Also, the thermal effectiveness depends on the Rayleigh number and the volume fraction of the nanoparticles

Citation

Hamza Mihoubi , , (2019), Improvement of Free Convection Heat Transfer in a Concentric Cylindrical Annulus Heat Exchanger Using Nanofluid, Mathematical Modelling of Engineering Problems, Vol:6, Issue:4, pages:8, International Information and Engineering Technology Association