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ISOPERIMETRIC PROBLEMS OF THE CALCULUS OF VARIATIONS WITH fractional derivatives

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Acta Mathematica Scientia 2012年第2期32卷 619-630页

作者： Ricardo Almeida Rui A.C.Ferreira Delfim F.M.Torres Center for Research and Development in Mathematics and Applications Department of MathematicsUniversity of Aveiro3810-193 AveiroPortugal Department of Mathematics Faculty of Engineering and Natural SciencesLusophone University of Humanities and Technologies1749-024 LisbonPortugal

In this article, we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide a... 详细信息

关键词： Calculus of variations fractional derivatives isoperimetric problems

New mathematical modelings of the human liver and hearing loss systems with fractional derivatives

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International Journal of Biomathematics 2023年第1期16卷 183-207页

作者： Mir Sajjad Hashemi Mohammad Partohaghighi Hijaz Ahmad Department of Mathematics Basic Science Faculty University of BonabP.O.Boc 55513-95133 BonabIran Department of Mathematics Clarkson University PotsdamNY13699USA Department of Basic Sciences University of Engineering and Technology Peshawar 25000 Pakistan Section of Mathematics International Telematic University Uninettuno Corso Vittorio Emanuele I 39Roma 00186Italy

fractional derivatives are significant mathematical instruments that have been practiced to model real phenomena in different areas of *** the current investigation study,we develop the Human Liver and Hearing Loss models by employing three fractional operators called Atangana-Baleanu-Caputo,Caputo and Caputo-Fabrizio *** numerical techniques regarding the basic theories of fractional analysis considered to obtain the approximate solutions of the offered ***,approximate results are presented for showing the efficacy of the methods during graphs of *** see the performance of the suggested models,different fractional orders are tested.

关键词： Numerical method fractional calculus fractional derivatives Human Liver model Hearing Loss model Lagrange interpolation.

The fractional derivatives of a Fractal Function

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Acta Mathematica Sinica,English Series 2006年第3期22卷 719-722页

作者： Kui YAO Wei Yi SU Song Ping ZHOU Department of Mathematics Nanjing University and PLA University of Sci-Tech Department of Mathematics Nanjing University Institute of Mathematics Zhejiang Sci-Tech University

The present paper investigates the fractional derivatives of Weierstrass function, proves that there exists some linear connection between the order of the fractional derivatives and the dimension of the graphs of Wei... 详细信息

关键词： Weierstrass function fractional derivatives dimensions of graphs of functions

fractional Noether's Theorems for El-Nabulsi's fractional Birkhoffian Systems in Terms of Riemann-Liouville derivatives

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Journal of Donghua University(English Edition) 2017年第1期34卷 14-20页

作者：宋传静张毅 College of Science Nanjing University of Science and Technology Nanjing 210094 China College of Civil Engineering Suzhou University of Science and Technology Suzhou 215011 China

The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional *** problem of the calculus of variations with fractional derivatives is a hot topic ***,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were ***,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations ***,an example is given to illustrate the methods and results appeared in this paper.

关键词： fractional Birkhoff equations transversality condition calculus of variations fractional derivatives Noether’s theorem

fractional Optical Solitons and fractional Noether’s Theorem with Ortigueira’s Centered derivatives

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Applied Mathematics 2016年第12期7卷 1340-1352页

作者： Jorge Fujioka Manuel Velasco Argel Ramírez Instituto de Física Departamento De Física-Química Universidad Nacional Autónoma de México México D.F. México nstituto de Física Departamento De Física-Química Universidad Nacional Autónoma de México México D.F. México Centro de Ciencias de la Atmósfera Universidad Nacional Autónoma de México México D.F. México

This paper shows that the centered fractional derivatives introduced by Manuel Duarte Ortigueira in 2006 are useful in the description of optical solitons. It is shown that we can construct a fractional extension of the nonlinear Schrödinger (NLS) equation which incorporates Ortigueira’s derivatives and has soliton solutions. It is also shown that this fractional NLS equation has a Lagrangian density and can be derived from a variational principle. Finally, a fractional extension of Noether’s theorem is formulated to determine the conserved quantities associated to the invariances of the action integral under infinitesimal transformations.

关键词： fractional derivatives Centered derivatives Noether’s Theorem Ortigueira Optical Solitons

Analysis of Magnetic Resistive Flow of Generalized Brinkman Type Nanofluid Containing Carbon Nanotubes with Ramped Heating

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Computers, Materials & Continua 2021年第4期67卷 1069-1084页

作者： Muhammad Saqib Ilyas Khan Sharidan Shafie Ahmad Qushairi Mohamad El-Sayed M.Sherif Department of Mathematical Sciences Faculty of ScienceUniversiti Teknologi MalaysiaJohor Bahru81310Malaysia Faculty of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh CityVietnam Center of Excellence for Research in Engineering Materials(CEREM) King Saud UniversityAl-Riyadh11421Saudi Arabia Department of Physical Chemistry Electrochemistry and Corrosion LaboratoryNational Research CentreCairo12622Egypt

In recent times,scientists and engineers have been most attracted to electrically conducted nanofluids due to their numerous applications in various fields of science and *** example,they are used in cancer treatment(hyperthermia),magnetic resonance imaging(MRI),drugdelivery,and magnetic refrigeration(MR).Bearing in mind the significance and importance of electrically conducted nanofluids,this article aims to study an electrically conducted water-based nanofluid containing carbon nanotubes(CNTs).CNTs are of two types,single-wall carbon nanotubes(SWCNTs)and multiple-wall carbon nanotubes(MWCNTs).The CNTs(SWCNTs and MWCNTs)have been dispersed in regular water as base fluid to form waterCNTs *** Brinkman Type nanofluid model is developed in terms of time-fractional *** ramped heating and sinusoidal oscillations conditions have been taken at the *** model has been solved for exact analytical solutions via the fractional Laplace transform *** exact solutions have been graphically studied to explore the physics of various pertinent flow parameters on velocity and temperature *** empirical results reveal that the temperature and velocity fields decreased with increasing values of fractional parameters due to variation in thermal and momentum boundary *** is also indicated that the isothermal velocity and temperature are higher than ramped velocity and temperature.

关键词： Nanofluid fractional derivatives Brinkman type fluid exact solutions

Diffusion Based Channel Gains Estimation in WSN Using fractional Order Strategies

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Computers, Materials & Continua 2022年第2期70卷 2209-2224页

作者： Nasir Mahmud Khokhar Muhammad Nadeem Majeed Syed Muslim Shah Department of Computer Engineering University of Engineering and TechnologyTaxila47050Pakistan Punjab University College of Information Technology University of PunjabLahore54000Pakistan Department of Electrical Engineering Capital University of Science and TechnologyIslamabad44000Pakistan

In this study,it is proposed that the diffusion least mean square(LMS)algorithm can be improved by applying the fractional order signal processing *** of Caputo’s fractional derivatives are considered in the optimization of cost *** is suggested to derive a fractional order variant of the diffusion LMS *** applicability is tested for the estimation of channel parameters in a distributed environment consisting of randomly distributed sensors communicating through wireless *** topology of the network is selected such that a smaller number of nodes are *** the network,a random sleep strategy is followed to conserve the transmission power at the *** proposed fractional ordermodified diffusionLMS algorithms are applied in the two configurations of combine-then-adapt and *** average squared error performance of the proposed algorithms along with its traditional counterparts are evaluated for the estimation of the Rayleigh channel *** proof of convergence is provided showing that the addition of the nonlinear term resulting from fractional derivatives helps adjusts the autocorrelation matrix in such a way that the spread of its eigenvalues *** increases the convergence as well as the steady state response even for the larger step *** results are shown for different number of nodes and fractional *** simulation results establish that the accuracy of the proposed scheme is far better than its classical counterparts,therefore,helps better solves the channel gains estimation problem in a distributed wireless *** algorithm has the potential to be applied in other applications related to learning and adaptation.

关键词： Diffusion strategies distributed channel gains fractional derivatives mean squared error

Heat Transfer in MHD Flow of Maxwell Fluid via fractional Cattaneo-Friedrich Model:A Finite Difference Approach

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Computers, Materials & Continua 2020年第12期65卷 1959-1973页

作者： Muhammad Saqib Hanifa Hanif T.Abdeljawad Ilyas Khan Sharidan Shafie Kottakkaran Sooppy Nisar Department of Mathematical Sciences Faculty of ScienceUniversiti Teknologi MalaysiaJohor Bahru81310Malaysia Department of Mathematics Sardar Bahadur Khan Women’s UniversityQuettaPakistan Department of Mathematics and General Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Computer Science and Information Engineering Asia UniversityTaichung40402Taiwan Faculty of Mathematics and Statistics Ton Duc Thang UniversityHo Chi Minh CityVietnam Department of Mathematics College of Arts and SciencesPrince Sattam bin Abdulaziz UniversityWadi Aldawaser11991Saudi Arabia

The idea of fractional derivatives is applied to several problems of viscoelastic ***,most of these problems(fluid problems),were studied analytically using different integral transform techniques,as most of these problems are *** idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential *** importantly,in the nonlinear problems,either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems(without developing the fractional model even using artificial replacement)are *** problems were mostly solved for steady-state fluid *** the present article,studied unsteady nonlinear non-Newtonian fluid problem(Cattaneo-Friedrich Maxwell(CFM)model)and the fractional model are developed starting from the fractional constitutive equations to the fractional governing equations;in other words,the artificial replacement of the classical derivatives with fractional derivatives is not done,but in details,the fractional problem is modeled from the fractional constitutive *** exactly two-dimensional magnetic resistive flow in a porous medium of fractional Maxwell fluid(FMF)over an inclined plate with variable velocity and the temperature is *** Caputo time-fractional derivative model(CFM)is used in the governing *** proposed model is numerically solved via finite difference method(FDM)along with L1-scheme for *** numerical results are presented in various *** results indicated that the fractional parameters significantly affect the temperature and velocity *** is noticed that the temperature field increased with an increase in the fractional ***,the effect of fractional parameters is opposite on the velocity field near the ***,this trend became like that of the temperature profile,away from the ***,

关键词： Viscoelastic fluid Cattaneo-Friedrich Maxwell model variable heating magnetohydrodynamic(MHD) porous medium fractional derivatives

Modeling the dynamical behavior of the interaction of T-cells and human immunodeficiency virus with saturated incidence

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Communications in Theoretical Physics 2024年第3期76卷 1-14页

作者： Salah Boulaaras Rashid Jan Amin Khan Ali Allahem Imtiaz Ahmad Salma Bahramand Department of Mathematics College of ScienceQassim UniversityBuraydah51452Saudi Arabia Institute of Energy Infrastructure(IEI) Department of Civil EngineeringCollege of EngineeringUniversiti Tenaga Nasional(UNITEN)Putrajaya CampusJalan IKRAM-UNITEN43000 KajangSelangorMalaysia Department of Mathematics University of SwabiSwabi 23561Pakistan Department of Mathematics College of SciencesQassim UniversitySaudi Arabia Institute of Informatics and Computing in Energy(IICE) Universiti Tenaga NasionalKajangSelangorMalaysia Department of Political Science Bacha Khan University CharsaddaCharsadda 24420KPK Pakistan

In the last forty years,the rise of HIV has undoubtedly become a major concern in the field of public health,imposing significant economic burdens on affected ***,it becomes imperative to undertake comprehensive investigations into the mechanisms governing the dissemination of HIV within the human *** this work,we have devised a mathematical model that elucidates the intricate interplay between CD4^(+)T-cells and viruses of HIV,employing the principles of fractional *** production rate of CD4^(+)T-cells,like other immune cells depends on certain factors such as age,health status,and the presence of infections or ***,we incorporate a variable source term in the dynamics of HIV infection with a saturated incidence rate to enhance the precision of our *** introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV *** facilitate a deeper understanding of our system,we present an iterative scheme that elucidates the trajectories of the solution pathways of the *** show the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the *** addition to this,we present the phase portrait and the oscillatory behavior of the system with the variation of different input *** information can be utilized to predict the long-term behavior of the system,including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.

关键词： HIV infection fractional-calculus dynamics of HIV iterative scheme dynamical behaviour mathematical model fractional derivatives