Fethi Bin Muhammad Belgacem

Public Authority for Applied Education and Training | PAAET · Mathematics

Sumudu transform integral equation is solved by continuous integration by parts to obtain its definition for trigonometric functions, where the transform variable is included as factor of f(t) and summing the integrated coeffecients evaluated at zero yields the image of trigonometric functions. The obtained result is inverted to show the expansion...

Just in case, you needed a chronology of the Sumudu and Natural Transforms you can download it form my ResearchGate Account: https://www.researchgate.net/profile/Fethi_Belgacem

This research article aims at treating the transverse electromagnetic wave propagation in lossy media, labeled TEMP. Following the trail of works by Hussain and Belgacem, and Belgacem et al. towards getting the transient electric field solution of Maxwell’s equations, here we seek Sumudu transform based solution for transient magnetic field. Moreov...

In this paper, we investigate and use the new modified exp(−Ω (ξ ))-expansion method, (MEM). We apply the new MEM to nonlinear long–short-wave interaction systems (NLSWIS). Among our findings are sets of solutions including, but not limited to, new hyperbolic, complex, and dark soliton solutions. Not only is MEM shown to be highly adaptable for par...

In this research article, we present theoretical techniques that can be used to investigate and comprehend the convergence behavior patterns of single parent evolution strategies. In the process, we determine instances of divergence or prove log-linear convergence and estimate the related speed, for a single parent evolution strategies class. The t...

In this paper, we propose a new dynamical system model pertaining to Dengue transmission, and investigate its consequent morphology. We present and study various ramifications of our mathematical model for Dengue spread, encapsulated in a spatio-temporal differential system made of reaction–diffusion equations. Diffusion terms are incorporated into...

This article presents some important results of conformable fractional partial derivatives. The conformable triple Laplace and Sumudu transform are coupled with the Adomian decomposition method where a new method is proposed to solve nonlinear partial differential equations in 3-space. Moreover, mathematical experiments are provided to verify the p...

In this paper, we introduced a new fractional derivative operator based on Lonezo Hartely function, which is called G-function. With the help of the operator, we solved a fractional diffusion equations. Some applications related to the operator is also discussed as form of corollaries.

The basic motivation of the present study is to apply the local fractional Sumudu variational iteration method (LFSVIM) for solving nonlinear wave-like equations with variable coefficients and within local fractional derivative. The derivatives operators are taken in the local fractional sense. The results show that the LFSVIM is an appropriate me...

The extended BKP-Boussinesq equation is considered to construct abundant breather waves, multi-shocks waves and localized excitation solutions. We first transform the original model to its bilinear form through a logarithmic transformation relation. Then, by setting a simple ansatz as a combinations of exponential and sinusoidal functions to obtain...

The monotonicity and the representation formulae of generalized \(\mathtt {k}\)-Bessel functions, \(W_{\nu ,c}^{\mathtt {k}}\), studied by SR Mondal. This paper establishes the image formulae and then extract the solutions for fractional kinetic equations, involving \(W_{\nu ,c}^{\mathtt {k}}\) utilizing their Sumudu transforms. Some significant pa...

Background: Aphasia is an intellectual disability that provokes language impairment. Among its various nuances, we chose dysgraphia, which affects writing skills. As language is not separate from the body our interdisciplinary approach brings a perspective that transforms research into effective social work, developing methods to interfere in the l...

In this paper, we examine the Zika virus transmission for human and mosquito populations. At the first time, a compartment model based on two populations, humans and mosquitoes, are proposed and analyzed quantitatively using the stability theory of the differential equations. In the second time, a nonhuman primate(monkey) is considered, we prove th...

In this paper, we examine the Zika virus transmission for human and mosquito populations. At the first time, a compartment model based on two populations, humans and mosquitoes, are proposed and analysed quantitatively using the stability theory of the differential equations. In the second time, a non-human primate (monkey) is considered, we prove...

In this article, we have studied the convergence properties of double Sumudu transformation, and we presented the results in the form of theorems on convergence, absolute convergence, and uniform convergence of Double Sumudu transformation. The Double Sumudu transform of double Integral has also been discussed for integral evaluation. Finally, we h...

This article makes a qualitative analysis of what constitutes the academic work in its overlapping elements and processes. There is a joint analysis of theory and facts based on discourse analysis theory to observe intrinsic aspects that put creativity as an essential product of academic work, and extrinsic aspects necessary to establish trust and...

Análise Qualitativa do Trabalho Acadêmico. Este artigo faz uma análise qualitativa do que caracteriza o trabalho acadêmico em seus processos e elementos que se sobrepõem. Análise e teoria caminham juntas com base na teoria da Análise do Discurso para observar aspectos in-trínsecos, que colocam a criatividade como produto essencial do trabalho acadê...

In this paper, we examine the Zika virus transmission for human and mosquito populations. At the first time, a compartment model based on two populations, humans and mosquitoes, are proposed and analyzed quantitatively using the stability theory of the differential equations. In the second time, a nonhuman primate (monkey) is considered, we prove t...

Aphasia is an intellectual disability that provokes language impairment. Among its various nuances, we chose dysgraphia, which affects writing skills. As language is not separate from the body our interdisciplinary approach brings a perspective that transforms research into effective social work, developing methods to interfere in the language proc...

In this paper, we introduce a combined form of the discrete Sumudu transform method with the discrete homotopy perturbation method to solve linear and nonlinear partial difference equations. This method is called the discrete homotopy perturbation Sumudu transform method(DHPSTM). The results reveal that the introduced method is very efficient, simp...

In this research article, the Discrete Inverse Sumudu Transform (DIST) multiple shifting properties are used to design a methodology for solving ordinary differential equations. We say ”Discrete” because it acts on the Taylor or Mclaurin series of the function when any. The algorithm applied to solve the Whittaker and Zettl equations and get their...

In the present research article, we investigate the solutions for fractional kinetic equations, involving k-Struve functions, some of the salient properties of which we present. The method used is Laplace transform based. The methodology and results can be adopted and extended to various related fractional problems in mathematical physics.

This article is part of a project in Mathematical and Linguistic Foundations for Intuitive Decisions. It explores decision-making processes in different realities: virtual and real. Linguistic foundations are bases to distinguish these realities, explained through the Discourse Analysis (DA) theory, which takes language effects as caused by ideolog...

We aim to relate the time dimension to the functioning of ideology and language, which interferes with the constitution of the subject. The time dimension, as an anticipatory mechanism, dictates to the subject an artificial creation of reality. We understand the subject as the "basis" that guarantees the non-crystallization of this virtual reality...

In the present work, enhancement of convective heat transfer rate in three-dimensional U-shaped enclosures using nanofluids is numerically investigated. Two different types of nanoparticles, namely, Cu, and Al2O3, with pure water, are the considered single-phase nanofluids. Natural convection and geometric parameter effects on the averaged Nusselt...

In the present paper, the explicit solutions of some local fractional partial differential equations are constructed through the integration of local fractional Sumudu transform and homotopy perturbation such as local fractional dissipative and damped wave equations. The convergence aspect of this technique is also discussed and presented. The obta...

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given...

This is simply a Pointer to where you can download the JCR 2017 PDF.

Reaching a Permutation of Kaprekar's Number (6174), 1674 Google Scholar Citations on February 17th, 2018.

In this paper, we have considered the problem that all solutions of the general integro quasi-differential equation [τ-λI]y(t) = wF(t;y;S(y)) are bounded and Lw² - bounded on [0,b) under suitable conditions on the integrand function F, where τ is a general quasi-differential expression of order n with complex coefficients and S(y) is the Sumudu tra...

Finding the solutions of some fractional differential equations, many of which used to be hard if not nearly untractable, is among the hottest quests in the fractional calculus field, nowadays. Doing so for the fractional distributed order reaction-diffusion equation is the very target of this paper. Recently, by applying integral transforms, Fouri...

In this research work, Dixon elliptic functions having modulus α = 0 for higher arbitrary powers, are treated with the Sumudu transform. From the resulting three term recurrences, product of the associated continued fractions expansions are given. Then, corresponding Hankel determinants are computed. Moreover we obtain generalized results including...

In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct variou...

In this paper, we pursue and investigate the solutions for fractional kinetic equations, involving Bessel-Struve function by means of their Sumudu transforms. In the process, one Important special case is then revealed, and analyzed. The results obtained in terms of Bessel-Struve function are rather general in nature and can easily construct variou...

Recently, representation formulae and monotonicity properties of generalized k-Bessel functions, Wk v,c., were established and studied by SR Mondal [24]. In this paper, we pursue and investigate some of their image formulae. We then extract solutions for fractional kinetic equations, involving Wk v,c, by means of their Sumudu transforms. In the pro...

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various re...

The universe [...] cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics (Galileo Galilei, The Assayer, 1623) The mathematical foundations in the Sciences bring reliability and solidity and they can be applied to a vast range of pheno...

The Natural transform is used to solve fractional differential equations for various values of fractional degrees α, and various boundary conditions. Fractional diffusion problems solutions are analyzed, followed by Stokes–Ekman boundary thickness problem. Furthermore, the Sumudu transform is applied for fluid flow problems, such as Stokes, Rayleig...

Preface In continuation with similar tasks performed with the special issue of the journal of Nonlinear Studies , [1], now comes the turn of the Mathematics in Engineering, Science and Aerospace journal, endearingly abbreviated as MESA, for Table in Spanish. The purpose of this issue as indicated by the title was to provide in this Table of papers,...

In this present study, we investigate solutions for fractional kinetic equations, involving k-Struve functions using Sumudu transform. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.

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The Sumudu transform of time function f (t) is computed by making the transform variable u of Sumudu as factor of function f (t) and then integrated against exp(−t). Being a factor in the original function f (t), becomes f (ut) preserves units and dimension. This preservation property distinguishes Sumudu from other integral transforms. With obtain...

The Sumudu transform is applied to arbitrary powers Dumont bimodular Jacobi elliptic functions. The resulting three term recurrence relations are expanded as product of associated continued fraction. From the coefficients of continued fractions, Hankel determinants are calculated. With already established modular transformation, The Sumudu transfor...

In the present paper, we apply the Sumudu transform to the Bernoulli generic function (BGF), then the properties of this transformation are examined, in the goal of re-extract some properties of Bernoulli Numbers and Polynomials. we show an excellent correlation between the Sumudu of BGF and Trigamma function.

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fracti...

This research paper treats fractional kinetic equations using the Sumudu transform operator. The exact solutions obtained are presented in terms of Struve functions of four parameters. By way of obtaining solutions some novel and useful and novel kinetic theorems are presented in light of the Sumudu properties. Results obtained in this study may be...

MESA JOURNAL SPECIAL ISSUE ANNOUNCEMENT for March 2017, Vol. 8, Issue No.2,

This research article aims at treating the transverse electromagnetic wave propagation in lossy medium problem, labeled TEMP. Indeed, following the trail of works by Hussain and Belgacem, and Belgacem et al. towards getting the transient electric field solution, in this paper we alternatively Sumudu treat Maxwells equations, only to exhibit the ran...

Wireless networks are often vulnerable to all kind of security attacks due to its open structure. i.e. free to join and leave the network. Much of the attacks are formed as intentional interference, generally called as jamming, which can be used as a launchpad for mounting DoS attacks over Wireless Networks. Thus for, a typical jamming attacks were...

In this research paper we present a new hybrid analytico-numerical scheme for solving linear quadratic optimal control problems. The method is based on a new Bernoulli wavelet ma- trix. After presenting relevant properties of the Bernoulli wavelet, we apply its connected operational matrix to derivatives. The solution is then obtained by reducing t...

In the present research article, we investigate solutions for fractional kinetic equations, involving k-Struve functions, some of the salient properties of which we present. The method used is Laplace transform based. the methodology and results can be adopted and extended to various related fractional problems in mathematical physics.