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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

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

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

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

Theory and Semi-Analytical Study of Micropolar Fluid Dynamics through a Porous Channel

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Computer Modeling in Engineering & Sciences 2023年第8期136卷 1473-1486页

作者： Aziz Khan Sana Ullah kamal shah Manar A.Alqudah Thabet Abdeljawad Fazal Ghani Department of Mathematics and Sciences Prince Sultan UniversityP.O.Box 66833Riyadh11586Saudi Arabia Department of Mathematics Abdul Wali Khan UniversityMardanP.O.Box 23200Khyber Pakhtunkhwa23200Pakistan Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtunkhwa18000Pakistan Department of Mathematical Sciences Faculty of SciencesPrincess Nourah bint Abdurahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia Department of Medical Research China Medical UniversityTaichung40402Taiwan

In this work,We are looking at the characteristics of micropolar flow in a porous channel that’s being driven by suction or *** working of the fluid is described in the *** can reduce the governing nonlinear partial differential equations(PDEs)to a model of coupled systems of nonlinear ordinary differential equations using similarity variables(ODEs).In order to obtain the results of a coupled system of nonlinear ODEs,we discuss a method which is known as the differential transform method(DTM).The concern transform is an excellent mathematical tool to obtain the analytical series solution to the nonlinear *** observe beast agreement between analytical method and numerical method,we compare our result with the Rung-Kutta method of order four(RK4).We also provide simulation plots to the obtained result by using *** plots,we discuss the effect of different parameters which arise during the calculation of the flow model equations.

关键词： Mass transfer micropolar flow porous channel similarity variables differential transform method

Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

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Computer Modeling in Engineering & Sciences 2023年第8期136卷 1931-1950页

作者： Lakhlifa Sadek Otmane Sadek Hamad Talibi Alaoui Mohammed S.Abdo kamal shah Thabet Abdeljawad Laboratory of Engineering Sciences for Energy National School of Applied SciencesChouaib Doukkali UniversityEl Jadida10002Morocco Department of Mathematics Faculty of SciencesChouaib Doukkali UniversityEl Jadida10002Morocco Department of Mathematics Hodeidah UniversityAl-Hudaydah91911Yemen Department of Mathematics and Sciences Prince Sultan UniversityRiyadh11586Saudi Arabia Department of Mathematics University of MalakandChakdara Dir(L)Khyber Pakhtankhawa18000Pakistan Department of Medical Research China Medical UniversityTaichung40402Taiwan

In this work,we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019(COVID-19)with different hospitalization strategies for severe and mild cases and incorporate an awareness *** generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health ***,individuals with severe,mild symptoms and asymptomatically infected are also *** basic reproduction number(R0)and local stability of the disease-free equilibrium(DFE)in terms of R0 are ***,the uniqueness and existence of the solution are *** simulations are performed by using some real values of ***,the immunization of a sample of aware susceptible individuals in the proposed model to forecast the effect of the vaccination is also ***,an investigation of the effect of public awareness on transmission dynamics is one of our aim in this ***,a prediction about the evolution of COVID-19 in 1000 days is *** the qualitative theory of the existence of a solution,we use some tools of nonlinear analysis,including Lipschitz ***,for the numerical interpretation,we use the Adams-Moulton-Bashforth *** the numerical results are presented graphically.

关键词： Fractional calculus caputo derivatives COVID-19 reproduction number future prediction

Plants’Steroidal Saponins‑A Review on Its Pharmacology Properties and Analytical Techniques

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World Journal of Traditional Chinese Medicine 2022年第3期8卷 350-385页

作者： Sudha Porte Veenu Joshi kamal shah Nagendra Singh Chauhan Center for Basic Sciences Pt.Ravishankar Shukla UniversityRaipurChhattisgarhIndia Institute of Pharmaceutical Research GLA UniversityMathuraUttar PradeshIndia Drugs Testing Laboratory Avam Anusandhan KendraRaipurChhattisgarhIndia

The plant is a rich repository of useful secondary metabolites with profound medicinal ***,one type of bioactive compound,are amphitheatric glycosides with one and more hydrophilic sugar and hydrophobic steroidal and terpenoid *** former is known as steroidal saponin,and the latter is called terpenoid *** saponin is mostly distributed among monocotyledon families such as Asparagaceae,Amaryllidaceae,Dioscoreaceae,Smilacaceae,and *** though it is unusual,it could also be detected to some extent by dicotyledonous angiosperms,such as Plantaginaceae,Zygophyllaceae,Fabaceae,Asteraceae,and *** exhibits diverse pharmacological ability including antimicrobic,anti‑inflammatory,cAMP phosphodiesterase inhibitory,antiadipogenic,bactericide,cardioprotective,antitumor,antidiabetic,cytotoxic activity,antifungal,antiviral,antioxidant,and *** saponin timosaponin AIII from Anemarrhena asphodeloides has been found to possess antitumor ***,another steroidal sapogenin,has the potential of preventing neurological diseases by affecting different signaling pathways,increasing bone formation,and increasing antithrombotic *** A from Liriope platyphylla possesses anti‑inflammatory,antiasthma,and antiosteoclastogenic ***2 from Trillium tschonoskii exhibits anticancer *** cell cycle arrest and ROS‑dependent autophagy are induced by polyphyllin *** diverse biological activities of steroidal saponins are attributed to the variability of their structural *** of steroidal saponins in plant materials mainly utilizes classically and advances thin layer chromatography(TLC)on normal and reverses‑phase(high‑performance thin‑layer chromatography,densitometric TLC),gas chromatography,LC,UPLC,ultra‑high‑performance liquid chromatography(HPLC),supercritical fluid chromatography,and HPLC coupled to ultraviolet detector and diode array *** coupled with

关键词： Steroidal Saponins Glycosides Antitumour Antioxidant Analytical techniques

Targeting colorectal cancer using dietary flavonols

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Cancer Innovation 2024年第1期3卷 124-132页

作者： Nitin Dubey Nidhi Dubey Upendra Bhadoria kamal shah Nagendra Singh Chauhan IPS Academy College of Pharmacy IndoreMadhya PradeshIndia School of Pharmacy Devi Ahilya VishwavidyalayaIndoreMadhya PradeshIndia Institute of Pharmaceutical Research GLA UniversityMathuraUttar PradeshIndia Drugs Testing Laboratory Avam Anusandhan Kendra RaipurChhattisgarhIndia

Colorectal cancer is among the well-known forms of cancer and a prominent cause of cancer demises *** vitro experiments reinforced by animal studies,as well as epidemiological studies of human colorectal cancer propose that the growth of this disease can be moderated by eating *** intake including green vegetables and fruits may result in the reduction of colon cancer *** finding suggests that the combinations of dietary nutrients may deliver additive or synergistic effects and might be a powerful method to avoid or eradicate colon cancer beginning and/or *** are one of the most widespread dietary nutrients of the polyphenols-flavonoids and major constituent of Allium and Brassicaceae *** present in vegetables of Allium and Brassicaceae family are kaempferol,myricetin,quercetin,and *** flavonols are claimed to have antiproliferative activity in vivo and in vitro against colorectal *** objective of this review is to summarize the role of flavonols obtained from dietary sources in the prevention and treatment of colorectal cancer.

关键词： isorhamnetin kaempferol myricetin quercetin

Plants Used as Antihypertensive

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Natural Products and Bioprospecting 2021年第2期11卷 155-184页

作者： Tarawanti Verma Manish Sinha Nitin Bansal Shyam Raj Yadav kamal shah Nagendra Singh Chauhan I.K.Gujral Punjab Technical University(IKGPTU) JalandharPunjabIndia Laureate Institute of Pharmacy KathogJwalamukhiKangraHimachal PradeshIndia Department of Pharmacology ASBASJSM College of PharmacyBELARoparPunjabIndia Department of Chemistry S.P.Jain College(Veer Kunwar Singh UniversityAra)SasaramBiharIndia Institute of Pharmaceutical Research GLA UniversityNH#2MathuraUttar Pradesh 281406India Drugs Testing Laboratory Avam Anusandhan Kendra 1st Floor Govt.Ayurvedic Hospital BuildingGovt.Ayurvedic College Campus G.E.RoadRaipurChhattisgarh 492010India

Hypertension is a critical health problem and worse other cardiovascular *** is mainly of two types:Primary or essential hypertension and Secondary *** is the primary possibility feature for coronary heart disease,stroke and renal vascular *** medicines have been used for millions of years for the management and treatment of hypertension with minimum side *** aim to write this review is to collect information on the anti-hypertensive effects of natural herbs in animal studies and human involvement as well as to recapitulate the underlying mechanisms,from the bottom of cell culture and ex-vivo tissue *** to WHO,natural herbs/shrubs are widely used in increasing order to treat almost all the ailments of the human *** are the regular industrial units for the invention of chemical constituents,they used as immunity booster to enhance the natural capacity of the body to fight against different health prob-lems as well as herbal medicines and food products *** percent population of the world(around 5.6 billion people)consume medicines from natural plants for major health *** review provides a bird’s eye analysis primarily on the traditional utilization,phytochemical constituents and pharmacological values of medicinal herbs used to normalize hypertension *** sabdariffa,Allium sativum,Andrographis paniculata,Apium graveolens,Bidenspilosa,Camel-lia sinensis,Coptis chinensis,Coriandrum sativum,Crataegus spp.,Crocus sativus,Cymbopogon citrates,Nigella sativa,Panax ginseng,Salviaemiltiorrhizae,Zingiber officinale,Tribulus terrestris,Rauwolfiaserpentina,Terminalia arjuna etc.

关键词： Hypertension Antihypertensive herbs Blood pressure Vasodilatation Herbal medicines Blood pressure regulation