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Solution approximations for a mathematical model of relativistic electrons with beta derivative

Applied Mathematics(A Journal of Chinese Universities) 2024年第3期39卷 469-485页

作者： Ibrahim Yalcinkaya Orkun Tasbozan Ali Kurt hijaz ahmad Department of Mathematics and Computer Sciences Faculty of ScienceNecmettin Erbakan UniversityKonyaTurkey Department of Mathematics Faculty of Science and LiteratureHatay Mustafa Kemal UniversityHatayTurkey Department of Mathematics Faculty of SciencePamukkale UniversityDenizliTurkey Near East University Operational Research Center in HealthcareTRNC Mersin 10Nicosia99138Turkey Department of Mathematics Faculty of ScienceIslamic University of MadinahMadinahSaudi Arabia

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta *** this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are *** applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact *** advantage of this procedure is that discretization or normalization is not *** applying the mETF,the exact solutions are ***,by applying the HAM semi-analytical results for the considered equation are *** HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution ***,comparative graphical representations are given to show the effectiveness,reliability of the *** results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta *** study can bring a new perspective for studies on fractional differential *** the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and *** involves fractional *** the results may cause a new insight who studies on relativistic electron modelling.

关键词： Klein-Fock-Gordon(KFG)equation beta derivative semi-analytical solution exact solution

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Soliton solutions for nonlinear variable-order fractional Korteweg-de Vries(KdV)equation arising in shallow water waves

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Journal of Ocean Engineering and Science 2024年第1期9卷 50-58页

作者： Umair Ali hijaz ahmad Hanaa Abu-Zinadah Department of Applied Mathematics and Statistics Institute of Space TechnologyP.O.Box 2750Islamabad 44000Pakistan Near East University Operational Research Center in HealthcareNear East BoulevardPC:99138 Nicosia/Mersin 10Turkey Section of Mathematics International Telematic University UninettunoCorso Vittorio Emanuele II3900186 RomaItaly University of Jeddah College of ScienceDepartment of StatisticsJeddahSaudi Arabia

Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and *** present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical *** VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion *** ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact *** newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO *** VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical *** results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.

关键词： Space-time VO fractional KdV equation modiﬁed(G′/G)-expansion method VO Caputo fractional derivative generalized Riccati equation

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An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

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Computer Modeling in Engineering & Sciences 2024年第5期139卷 1829-1862页

作者： Rana Muhammad Zulqarnain Wen-Xiu Ma Imran Siddique hijaz ahmad Sameh Askar School of Mathematical Sciences Zhejiang Normal UniversityJinhua321004China Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700USA School of Mathematical and Statistical Sciences North-West UniversityMafikeng CampusMmabatho2735South Africa Department of Mathematics University of SargodhaSargodha40100Pakistan Section of Mathematics International Telematic University UninettunoCorso Vittorio Emanuele IIRoma00186Italy Near East University Operational Research Center in HealthcareNicosia/Mersin99138Turkey Department of Statistics and Operations Research College of ScienceKing Saud UniversityRiyadh11451Saudi Arabia

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and *** frequently search for new ideas and strategies to assist them in realizing sustainable *** of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making *** main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their *** operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other ***,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment ***,a statistical clarification of the planned method for green supplier selection is presented.

关键词： Interval-valued Pythagorean fuzzy soft set IVPFSIWA operator IVPFSIWG operator MCGDM SCM

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Manakov model of coupled NLS equation and its optical soliton solutions

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Journal of Ocean Engineering and Science 2024年第4期9卷 364-372页

作者： Esra Unal Yilmaz Farid Samsami Khodad Yesim Saglam Ozkan Reza Abazari A.E.Abouelregal Mayssam Tarighi Shaayesteh Hadi Rezazadeh hijaz ahmad Department of Mathematics Bolu Abant Izzet Baysal UniversityBoluTurkey Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Department of Mathematics Bursa Uludag UniversityBursaTurkey Department of Mathematics and Applications University of Mohaghegh ArdabiliArdabilIran Department of Mathematics College of Science and ArtsAl-QurayatJouf UniversitySaudi Arabia Basic Sciences Research Unit Jouf UniversitySaudi Arabia Amir Kabir University TehranIran Mathematics in Applied Sciences and Engineering Research Group Scientific Research CenterAl-Ayen UniversityNasiriyah 64001Iraq Section of Mathematics International Telematic University UninettunoCorso Vittorio Emanuele II39Roma 00186Italy

In the field of maritime transport,motion and energy,the dynamics of deep-sea waves is one of the major problems in ocean science.A mathematical modeling of dynamics of solitary waves in deep sea under the two-layer stratification leads to NLS equation,and consequently,the interaction two of them can be formulated by coupled NLS *** this work,extended auxiliary equation and the exp(−ω(χ))-expansion methods are employed to make the optical solutions of the Manakov model of coupled NLS *** methods used in this paper,in addition to providing the analysis of individual wave solutions,also provide general optical *** previously known solutions can be obtained by some special selections of parameters obtained by solving systems of algebraic *** this stage,it is more practical and convenient to apply methods with a symbolic calculation system.

关键词： Manakov model Extended auxiliary equation method Optical solutions Solitons

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An Efficient Meshless Method for Hyperbolic Telegraph Equations in (1 + 1) Dimensions

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Computer Modeling in Engineering & Sciences 2021年第8期128卷 687-698页

作者： Fuzhang Wang Enran Hou Imtiaz ahmad hijaz ahmad Yan Gu College of Mathematics and Statistics Xuzhou University of TechnologyXuzhou221018China College of Mathematics Huaibei Normal UniversityHuaibei235000China Department of Mathematics University of SwabiSwabi25000Pakistan Department of Basic Sciences University of Engineering and TechnologyPeshawar25000Pakistan College of Mathematics Qingdao UniversityQingdao266071China

Numerical solutions of the second-order one-dimensional hyperbolic telegraph equations are presented using the radial basis *** purpose of this paper is to propose a simple novel direct meshless scheme for solving hyperbolic telegraph *** is fulfilled by considering time variable as normal space *** this scheme,there is no need to remove time-dependent variable during the whole solution *** the numerical solution accuracy depends on the condition of coefficient matrix derived from the radial basis function *** propose a simple shifted domain method,which can avoid the full-coefficient interpolation matrix *** experiments performed with the proposed numerical scheme for several second-order hyperbolic telegraph equations are presented with some discussions.

关键词： Radial basis functions telegraph equation shifted domain method meshless method

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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.

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Modeling of Dark Solitons for Nonlinear Longitudinal Wave Equation in a Magneto-Electro-Elastic Circular Rod

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Sound & Vibration 2021年第3期55卷 241-251页

作者： Hulya Durur Asıf Yokuş Doğan Kaya hijaz ahmad Department of Computer Engineering Faculty of EngineeringArdahan UniversityArdahanTurkey Department of Mathematics Faculty of ScienceFirat UniversityElazigTurkey Department of Mathematics Istanbul Commerce UniversityIstanbulTurkey Department of Basic Sciences University of Engineering and TechnologyPeshawarPakistan

In this paper,sub equation and (1=G’)-expansion methods are proposed to construct exact solutions of a nonlinear longitudinal wave equation(LWE)in a magneto-electro-elastic circular *** proposed methods have been used to construct hyperbolic,rational,dark soliton and trigonometric solutions of the LWE in the magnetoelectro-elastic circular *** values are given to the parameters in the solutions obtained.3D,2D and contour graphs are presented with the help of a computer package *** attained by symbolic calculations revealed that these methods are effective,reliable and simple mathematical tool for finding solutions of nonlinear evolution equations arising in physics and nonlinear dynamics.

关键词： (1/G’)-expansion method sub equation method exact solution traveling wave solution nonlinear evolution equations

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Soliton solutions for time fractional ocean engineering models with Beta derivative

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Journal of Ocean Engineering and Science 2022年第5期7卷 444-448页

作者： Ibrahim Yalçınkaya hijaz ahmad Orkun Tasbozan Ali Kurt Department of Mathematics and Computer Sciences Faculty of ScienceNecmettin Erbakan UniversityKonyaTurkey Department of Basic Sciences University of Engineering and TechnologyPeshawarPakistan Department of Mathematics Faculty of Science and LiteratureHatay Mustafa Kemal UniversityHatayTurkey Department of Mathematics Faculty of Science and LiteraturePamukkale UniversityDenizliTurkey

In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean *** this aim modified extended tanh-function(mETF)is *** using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer *** to the chain rule,there is no further requirement for any normalization or *** derivative which involves fractional term is used in considered mathematical *** the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.

关键词： Symmetric regularized long wave equation Beta derivative Ostrovsky equation Analytical solution Soliton solutions Periodic wave solution

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A Mathematical Approach for Generating a Highly Non-Linear Substitution Box Using Quadratic Fractional Transformation

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Computers, Materials & Continua 2023年第11期77卷 2565-2578页

作者： Abid Mahboob Muhammad Asif Rana Muhammad Zulqarnain Imran Saddique hijaz ahmad Sameh Askar Department of Mathematics Division of Science and TechnologyUniversity of EducationLahorePakistan Department of Mathematics University of Management and TechnologySialkot Campus51310Pakistan School of Mathematical Sciences Zhejiang Normal UniversityJinhua321004China Department of Mathematics University of Management and TechnologyLahore54770Pakistan Section of Mathematics International Telematic University UninettunoCorso Vittorio Emanuele IIRoma39-00186Italy Department of Statistics and Operations Research College of ScienceKing Saud UniversityP.O.Box 2455Riyadh11451Saudi Arabia

Nowadays,one of the most important difficulties is the protection and privacy of confidential *** address these problems,numerous organizations rely on the use of cryptographic techniques to secure data from illegal activities and *** cryptographic ciphers use the non-linear component of block cipher to ensure the robust encryption process and lawful decoding of plain data during the decryption *** the designing of a secure substitution box(S-box),non-linearity(NL)which is an algebraic property of the S-box has great ***,the main focus of cryptographers is to achieve the S-box with a high value of *** this suggested study,an algebraic approach for the construction of 16×16 S-boxes is provided which is based on the fractional transformation Q(z)=1/α(z)^(m)+β(mod257)and finite *** technique is only applicable for the even number exponent in the range(2-254)that are not multiples of ***,we choose a quadratic fractional transformation,swap each missing element with repeating elements,and acquire the initial *** the second stage,a special permutation of the symmetric group S256 is utilized to construct the final S-box,which has a higher NL score of 112.75 than the Advanced Encryption Standard(AES)S-box and a lower linear probability score of *** addition,a tabular and graphical comparison of various algebraic features of the created S-box with many other S-boxes from the literature is provided which verifies that the created S-box has the ability and is good enough to withstand linear and differential *** different analyses,it is ensured that the proposed S-boxes are better than as compared to the existing *** these S-boxes can be utilized in the security of the image data and the text data.

关键词： Block cipher S-box data security fractional transformation

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An Artificial Intelligence Approach for Solving Stochastic Transportation Problems

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Computers, Materials & Continua 2022年第1期70卷 817-829页

作者： Prachi Agrawal Khalid Alnowibet Talari Ganesh Adel F.Alrasheedi hijaz ahmad Ali Wagdy Mohamed Department of Mathematics and Scientific Computing National Institute of Technology HamirpurHimachal Pradesh177005India Statistics and Operations Research Department College of ScienceKing Saud UniversityRiyadh11451Kingdom of Saudi Arabia Section of Mathematics International Telematic University UninettunoRoma00186Italy Operations Research Department Faculty of Graduate Studies for Statistical ResearchCairo UniversityGiza12613Egypt Wireless Intelligent Networks Center(WINC) School of Engineering and Applied SciencesNile UniversityGizaEgypt

Recent years witness a great deal of interest in artificial intelligence(AI)tools in the area of *** has developed a large number of tools to solve themost difficult search-and-optimization problems in computer science and operations ***,metaheuristic-based algorithms are a sub-field of *** study presents the use of themetaheuristic algorithm,that is,water cycle algorithm(WCA),in the transportation problem.A stochastic transportation problem is considered in which the parameters supply and demand are considered as random variables that follow the Weibull *** the parameters are stochastic,the corresponding constraints are *** are converted into deterministic constraints using the stochastic programming *** this study,we propose evolutionary algorithms to handle the difficulties of the complex high-dimensional optimization *** is influenced by the water cycle process of how streams and rivers flow toward the sea(optimal solution).WCA is applied to the stochastic transportation problem,and obtained results are compared with that of the new metaheuristic optimization algorithm,namely the neural network algorithm which is inspired by the biological nervous *** is concluded that WCA presents better results when compared with the neural network algorithm.

关键词： Artificial intelligence metaheuristic algorithm stochastic programming transportation problem water cycle algorithm weibull distribution

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