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Study of Fractional Order Dynamical System of Viral Infection Disease under Piecewise Derivative

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Computer Modeling in Engineering & Sciences 2023年第7期136卷 921-941页

作者： Kamal Shah Hafsa Naz thabet.abdeljawad Bahaaeldin Abdalla Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan

This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)*** focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical *** establish some qualitative results about the existence and uniqueness of the solution to the proposed *** utilizing the Newtonian polynomials interpolation technique,we recall a powerful algorithm to interpret the numerical findings for the aforesaid ***,we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to *** bats which are also known as flying foxes are one of the sources of transmission of NiV *** in this work,we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and *** present the approximate results for different compartments using different fractional *** using the piecewise derivative concept,we detect the crossover ormulti-steps behavior in the transmission dynamics of the mentioned ***,the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.

关键词： NiV disease fractional calculus piecewise derivative qualitative results newton polynomial RNA virus

Quasi Controlled K-Metric Spaces over C^(*)-Algebras with an Application to Stochastic Integral Equations

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Computer Modeling in Engineering & Sciences 2023年第6期135卷 2649-2663页

作者： Ouafaa Bouftouh Samir Kabbaj thabet.abdeljawad Aziz Khan Department of Mathematics Laboratory of Partial Differential EquationsAlgebra and Spectral GeometryFaculty of SciencesIbn Tofail UniversityKenitraBP 133Morocco Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan

Generally,the field of fixed point theory has attracted the attention of researchers in different fields of science and engineering due to its use in proving the existence and uniqueness of solutions of real-world dynamic models.C^(∗)-algebra is being continually used to explain a physical system in quantum field theory and statistical mechanics and has subsequently become an important area of *** concept of a C^(∗)-algebra-valued metric space was introduced in 2014 to generalize the concept of metric *** fact,It is a generalization by replacing the set of real numbers with a C^(∗)-*** that,this line of research continued,where several fixed point results have been obtained in the framework of C^(∗)-algebra valued metric,aswell as(more general)C^(∗)-algebra-valued b-metric spaces andC^(∗)-algebra-valued extended b-metric *** recently,based on the concept and properties of C^(∗)-algebras,we have studied the quasi-case of such spaces to give a more general notion of relaxing the triangular inequality in the asymmetric *** this paper,we first introduce the concept of C^(∗)-algebra-valued quasi-controlledK-metric spaces and prove some fixed point theorems that remain valid in this *** support our main results,we also furnish some exampleswhichdemonstrate theutility of ***,as an application,we useour results to prove the existence and uniqueness of the solution to a nonlinear stochastic integral equation.

关键词： C^(*)-algebra-valued quasi controlled K-metric spaces left convergence right convergence fixed point contraction

On Fuzzy Conformable Double Laplace Transform with Applications to Partial Differential Equations

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Computer Modeling in Engineering & Sciences 2023年第3期134卷 2163-2191页

作者： thabet.abdeljawad Awais Younus Manar A.Alqudah Usama Atta Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakaryia UniversityMultan60000Pakistan Department of Mathematical Sciences Faculty of SciencesPrincess Nourah Bint Abdulrahman UniversityRiyadh11671Saudi Arabia

The Laplace transformation is a very important integral transform,and it is extensively used in solving ordinary differential equations,partial differential equations,and several types of integro-differential *** purpose in this study is to introduce the notion of fuzzy double Laplace transform,fuzzy conformable double Laplace transform(FCDLT).We discuss some basic properties of *** obtain the solutions of fuzzy partial differential equations(both one-dimensional and two-dimensional cases)through the double Laplace *** demonstrate through numerical examples that our proposed method is very successful and convenient for resolving partial differential equations.

关键词： Fuzzy conformable laplace transform fuzzy double laplace transform fuzzy conformable double laplace transform fuzzy conformable partial differential equation

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

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Computer Modeling in Engineering & Sciences 2023年第6期135卷 2743-2765页

作者： Kamran Siraj Ahmad Kamal Shah thabet.abdeljawad Bahaaeldin Abdalla Department of Mathematics Islamia College PeshawarKhyber Pakhtoon KhwaPeshawar25120Pakistan Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science *** the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by ***,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real *** this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main ***,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo ***,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace *** the solution of the transformed equation is obtained in Laplace ***,the solution is converted into the real domain using numerical inversion of Laplace *** inversion methods are evaluated in this paper,and their convergence is also *** test problems are used to validate the inversion *** demonstrate our results with the help of tables and *** obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

关键词： Fractal-fractional differential equation power law kernel exponential decay kernel Mittag-Leffler kernel Laplace transform Euler’s method Talbot’s method Stehfest’s method

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

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Computer Modeling in Engineering & Sciences 2023年第8期136卷 1457-1472页

作者： Kamal Shah thabet.abdeljawad Fahd Jarad Qasem Al-Mdallal Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Mathematics Faculty of Arts and Sciences莂nkaya UniversityAnkara06790Turkey Department of Mathematical Sciences UAE UniversityAl-Ain15551United Arab Emirates

This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical *** the proposed study,we consider the model under the conformable fractional order derivative(CFOD).We investigate the mentioned dynamical system for the existence and uniqueness of at least one ***,Schauder and Banach fixed point theorems are utilized to prove our ***,an algorithm for the approximate analytical solution to the proposed problem has been *** this regard,the conformable fractional differential transform(CFDT)technique is used to compute the required results in the form of a *** Matlab-16,we simulate the series solution to illustrate our results ***,a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.

关键词： Prey predator model existence results conformable fractional differential transform

Numerical Solutions of Fractional Variable Order Differential Equations via Using Shifted Legendre Polynomials

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Computer Modeling in Engineering & Sciences 2023年第2期134卷 941-955页

作者： Kamal Shah Hafsa Naz thabet.abdeljawad Aziz Khan Manar A.Alqudah Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Mathematical Sciences Faculty of SciencesPrincess Nourah bint Abdurahman UniversityRiyadh11671Saudi Arabia

In this manuscript,an algorithm for the computation of numerical solutions to some variable order fractional differential equations(FDEs)subject to the boundary and initial conditions is *** use shifted Legendre polynomials for the required numerical algorithm to develop some operational ***,operational matrices are constructed using variable order differentiation and *** are finding the operationalmatrices of variable order differentiation and integration by omitting the discretization of *** the help of aforesaid matrices,considered FDEs are converted to algebraic equations of Sylvester ***,the algebraic equations we get are solved with the help of mathematical software like Matlab or Mathematica to compute numerical *** examples are given to check the proposed method’s accuracy and graphical *** and numerical solutions are also compared in the paper for some *** efficiency of the method can be enhanced further by increasing the scale level.

关键词： Operational matrices shifted legendre polynomials FDEs variable order

A Theoretical Investigation of the SARS-CoV-2Model via Fractional Order Epidemiological Model

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Computer Modeling in Engineering & Sciences 2023年第5期135卷 1295-1313页

作者： Tahir Khan Rahman Ullah thabet.abdeljawad Manar A.Alqudah Faizullah Faiz Department of Mathematics and Statistics Woman UniversitySwabiKhyber Pakhtunkhwa23501Pakistan Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Mathematical Sciences Faculty of SciencesPrincess Nourah Bint Abdulrahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia Department of Basic Sciences and Humanities College of Electrical and Mechanical EngineeringNational University of Sciences and Technology(NUST)Islamabad44320Pakistan

We propose a theoretical study investigating the spread of the novel coronavirus(COVID-19)reported inWuhan City of China in *** develop a mathematical model based on the novel corona virus’s characteristics and then use fractional calculus to fractionalize *** fractional order epidemicmodels have been formulated and analyzed using a number of iterative and numerical approacheswhile the complications arise due to singular *** use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular ***,to analyze the existence and uniqueness,we will use the well-known fixed point *** also prove that the considered model has positive and bounded *** also draw some numerical simulations to verify the theoretical work via graphical *** believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.

关键词： Fractional epidemiological model for corona virus disease caputo-fabrizio operator numerical simulation

On Riemann-Type Weighted Fractional Operators and Solutions to Cauchy Problems

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Computer Modeling in Engineering & Sciences 2023年第7期136卷 901-919页

作者： Muhammad Samraiz Muhammad Umer thabet.abdeljawad Saima Naheed Gauhar Rahman Kamal Shah Department of Mathematics University of SargodhaP.O.Box 40100Sargodha40100Pakistan Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan Department of Mathematics and Statistics Hazara University MansehraMansehra21300Pakistan Department of Mathematics University of MalakandChakdara Dir(L)KPK18000Pakistan

In this paper,we establish the new forms of Riemann-type fractional integral and derivative *** novel fractional integral operator is proved to be bounded in Lebesgue space and some classical fractional integral and differential operators are obtained as special *** properties of new operators like semi-group,inverse and certain others are discussed and its weighted Laplace transform is *** integro-differential freeelectron laser(FEL)and kinetic equations are *** solutions to these new equations are obtained by using the modified weighted Laplace *** Cauchy problem and a growth model are designed as applications along with graphical ***,the conclusion section indicates future directions to the readers.

关键词： Weighted fractional operators weighted laplace transform integro-differential free-electron laser equation kinetic differ-integral equation

Utilization of Machine Learning Methods in Modeling Specific Heat Capacity of Nanofluids

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Computers, Materials & Continua 2022年第1期70卷 361-374页

作者： Mamdouh El Haj Assad Ibrahim Mahariq Raymond Ghandour Mohammad Alhuyi Nazari thabet.abdeljawad Sustainable and Renewable Energy Engineering Department University of SharjahP.O.Box 27272SharjahUAE College of Engineering and Technology American University of theMiddle EastKuwait Faculty of New Sciences and Technologies University of TehranTehranIran 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 UniversityTaichungTaiwan

Nanofluids are extensively applied in various heat transfer mediums for improving their heat transfer characteristics and hence their *** heat capacity of nanofluids,as one of the thermophysical properties,performs principal role in heat transfer of thermal mediums utilizing *** this regard,different studies have been carried out to investigate the influential factors on nanofluids specific ***,several regression models based on correlations or artificial intelligence have been developed for forecasting this property of *** the current review paper,influential parameters on the specific heat capacity of nanofluids are ***,the proposed models for their forecasting and modeling are *** to the reviewed works,concentration and properties of solid structures in addition to temperature affect specific heat capacity to large extent and must be considered as inputs for the ***,by using other effective factors,the accuracy and comprehensive of the models can be ***,some suggestions are offered for the upcoming works in the relevant topics.

关键词： Specific heat capacity nanofluid artificial neural network concentration