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Fractional approach for mathematical model of phytoplankton-toxic phytoplankton-zooplankton system with Mittag-Leffler kernel

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International Journal of Biomathematics 2023年第3期16卷 195-218页

作者： p.veeresha Lanre Akinyemi Department of Mathematics Centre for Mathematical Needs CHRIST(Deemed to be University)Bengaluru 560029India Department of Mathematics Lafayette College EastonPennsylvaniaUSA

The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy analysis transform method(q-HATM)is *** projected system exemplifies three components(namely,zooplankton,toxic-phytoplankton as well as phytoplankton)and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on *** projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana-Baleanu(AB)*** equilibrium points and stability have been discussed with the assistance of the Routh-Hurwitz rule in this work within the frame of generalized *** fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model,and we consider five different initial conditions for the projected ***,the physical nature of the achieved solution has been captured for fractional order,external force and diverse *** achieved consequences explicate that the proposed solution method is highly methodical,easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology.

关键词： Toxic-phytoplankton q-HATM zooplankton stability analysis Atangana-Baleanu derivative Laplace transform

Analysis of Lakes pollution model with Mittag-Leffler kernel

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Journal of Ocean Engineering and Science 2020年第4期5卷 310-322页

作者： D.G.prakasha p.veeresha Department of Mathematics Faculty of ScienceDavangere UniversityShivagangothriDavangere-577007KarnatakaIndia Department of Mathematics Karnatak UniversityDharwad-580003KarnatakaIndia

The pivotal aim of the present investigation is to find an approximate analytical solution for the system of three fractional differential equations describing the Lakes pollution using q-homotopy analysis transform method(q-HATM).We consider three different cases of the considered model namely,periodic input model,exponentially decaying input model,and linear input *** considered scheme is unifications of q-homotopy analysis technique with Laplace transform(LT).To illustrate the existence and uniqueness for the projected model,we consider the fixed point *** preciously,we scrutinized the behaviour of the obtained solution for the considered model with fractional-order,in order to elucidate the effectiveness of the proposed ***,for the different fractional-order and parameters offered by the considered method,the physical natures have been *** obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems.

关键词： Lakes system Atangana-Baleanu derivative Laplace transform Fixed point theorem q-Homotopy analysis method

An efficient technique for two-dimensional fractional order biological population model

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第1期11卷 96-112页

作者： p.veeresha D.G.prakasha Department of Mathematics Karnatak University Dharwad 580003India Department of Mathematics Faculty of Science Davangere University ShivagangothriDavangere 577007India

In this paper,we find the solutions for two-dimensional biological population model having fractional order using fractional natural decomposition method(FNDM).The proposed method is a graceful blend of decomposition scheme with natural transform,and three examples are considered to validate and illustrate its *** nature of FNDM solution has been captured for distinct arbitrary *** order to illustrate the proficiency and reliability of the considered scheme,the numerical simulation has been *** obtained results illuminate that the considered method is easy to apply and more effective to examine the nature of multi-dimensional differential equations of fractional order arisen in connected areas of science and technology.

关键词： Caputo fractional derivative decomposition method biological population model natural transform

Regarding on the Fractional Mathematical Model of Tumour Invasion and Metastasis

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Computer Modeling in Engineering & Sciences 2021年第6期127卷 1013-1036页

作者： p.veeresha Esin Ilhan D.G.prakasha Haci Mehmet Baskonus Wei Gao Department of Mathematics CHRIST(Deemed to be University)Bengaluru560029India Faculty of Engineering and Architecture Kirsehir Ahi Evran UniversityKirsehir40500Turkey Department of Mathematics Faculty of ScienceDavangere UniversityShivagangothriDavangere577007India Department of Mathematics and Science Education Faculty of EducationHarran UniversitySanliurfa63050Turkey School of Information Science and Technology Yunnan Normal UniversityKunming650500China

In this paper,we analyze the behaviour of solution for the system exemplifying model of tumour invasion and metastasis by the help of q-homotopy analysis transform method(q-HATM)with the fractional *** analyzed model consists of a system of three nonlinear differential equations elucidating the activation and the migratory response of the degradation of the matrix,tumour cells and production of degradative enzymes by the tumour *** considered method is graceful amalgamations of q-homotopy analysis technique with Laplace transform(LT),and Caputo–Fabrizio(CF)fractional operator is hired in the present *** using the fixed point theory,existence and uniqueness are *** validate and present the effectiveness of the considered algorithm,we analyzed the considered system in terms of fractional order with time and *** error analysis of the considered scheme is *** variations with small change time with respect to achieved results are effectively captured in *** obtained results confirm that the considered method is very efficient and highly methodical to analyze the behaviors of the system of fractional order differential equations.

关键词： Tumour cell invasion and metastasis q-homotopy analysis transform method Caputo–Fabrizio derivative

Regarding Deeper properties of the Fractional Order Kundu-Eckhaus Equation and Massive Thirring Model

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Computer Modeling in Engineering & Sciences 2022年第12期133卷 697-717页

作者： Yaya Wang p.veeresha D.G.prakasha Haci Mehmet Baskonus Wei Gao Department of Information Engineering Binzhou PolytechnicBinzhou256603China Centre for Mathematical Needs Department of MathematicsCHRIST(Deemed to be University)Bengaluru560029India Department of Mathematics Davangere UniversityShivagangothriDavangere577007India Department of Mathematics and Science Education Faculty of EducationHarran UniversitySanliurfa63050Turkey School of Information Science and Technology Yunnan Normal UniversityKunming650500China

In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring *** Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field *** fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform *** order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional ***,the behaviour of the obtained solution has been captured for diverse fractional *** obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.

关键词： Fractional Kundu-Eckhaus equation fractional natural decomposition method fractional massive Thirring model numerical method Caputo fractional derivative

A novel approach to study generalized coupled cubic Schrödinger-Korteweg-de Vries equations

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Journal of Ocean Engineering and Science 2024年第1期9卷 13-24页

作者： Lanre Akinyemi p.veeresha M.T.Darvishi Hadi Rezazadeh Mehmet Senol Udoh Akpan Department of Mathematics Lafayette CollegeEastonPAUSA Department of Mathematics Christ Deemed to be UniversityBengaluru 560029India Department of Mathematics Razi UniversityKermanshah 67149Iran Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Department of Mathematics Nev¸s ehir HacıBekta¸s Veli UniversityNev¸s ehirTurkey Drexel University Department of MathematicsPhiladelphiaPAUSA

The Kortewegde Vries(KdV)equation represents the propagation of long waves in dispersive media,whereas the cubic nonlinear Schrödinger(CNLS)equation depicts the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves.A model that couples these two equations seems in-triguing for simulating the interaction of long and short waves,which is important in many domains of applied sciences and engineering,and such a system has been investigated in recent *** work uses a modified Sardar sub-equation procedure to secure the soliton-type solutions of the generalized cubic nonlinear Schrödinger-Korteweg-de Vries system of *** various selections of arbitrary parameters in these solutions,the dynamic properties of some acquired solutions are represented graph-ically and *** particular,the dynamics of the bright solitons,dark solitons,mixed bright-dark solitons,W-shaped solitons,M-shaped solitons,periodic waves,and other soliton-type *** re-sults demonstrated that the proposed technique is highly efficient and effective for the aforementioned problems,as well as other nonlinear problems that may arise in the fields of mathematical physics and engineering.

关键词： CNLS equation Modiﬁed Sardar sub-equation method KdV equation Solitons Long and short waves

Solution for fractional potential KdV and Benjamin equations using the novel technique

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Journal of Ocean Engineering and Science 2021年第3期6卷 265-275页

作者： p.veeresha D.G.prakasha N.Magesh A.John Christopher Deepak Umrao Sarwe Department of Mathematics CHRIST(Deemed to be University)Bengaluru-560029India Department of Mathematics Faculty of ScienceDavangere UniversityShivagangothriDavangere-577007India p.G.and Research Department of Mathematics Govt.Arts College for MenKrishnagiri-635001India Department of Mathematics University of MumbaiKalinaSantacruz EastMumbai-400098India

In this paper,we find the solutions for fractional potential Korteweg-de Vries(p-KdV)and Benjamin equations using q-homotopy analysis transform method(q-HATM).The considered method is the mixture of q-homotopy analysis method and Laplace transform,and the Caputo fractional operator is considered in the present *** projected solution procedure manipulates and controls the obtained results in a large admissible ***,it offers a simple algorithm to adjust the convergence province of the obtained *** validate the q-HATM is accurate and reliable,the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and *** between the obtained solutions with the exact solutions exhibits that,the considered method is efficient and effective in solving nonlinear problems associated with science and technology.

关键词： potential KdV equation q-Homotopy analysis method Fractional Benjamin equation Laplace transform Ginzburg-Landau equation Caputo fractional operator

Unlocking hypoglycemia–associated brain microvascular dysfunction:critical insights from proteomic analysis

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Neural Regeneration Research 2025年第6期20卷 1707-1708页

作者： Siva S.V.p.Sakamuri Anil Sakamuri Department of Chemistry Auburn University at MontgomeryMontgomeryALUSA Vascular Biology Center and Department of Medicine Medical College of Georgia at Augusta UniversityAugustaGAUSA

Hypoglycemia-a critical complication linked to worsened brain function in diabetic subjects:Hypoglycemia is characterized by a decline in circulatory glucose levels below sta nda rd physiological *** hypoglycemia,classified as level 1 hypoglycemia,is defined by blood glucose levels below 70 mg/dL and can be effectively addressed through carbohydrate *** hypoglycemia,denoted by blood glucose levels less than 54 mg/dL,poses a life-threatening risk if left *** with type 1 and type 2 diabetes undergoing insulin treatment are particularly susceptible to hypoglycemia due to impaired counterregulatory mechanisms.

关键词： impaired intake critical

Small molecule inhibitor DDQ-treated hippocampal neuronal cells show improved neurite outgrowth and synaptic branching

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Neural Regeneration Research 2025年第9期20卷 2624-2632页

作者： Jangampalli Adi pradeepkiran priyanka Rawat Arubala p.Reddy Erika Orlov pHemachandra Reddy Department of Internal Medicine Texas Tech University Health Sciences CenterLubbockTXUSA Department of Nutritional Sciences College of Human SciencesTexas Tech UniversityLubbockTXUSA Department of pharmacology&Neuroscience Texas Tech University Health Sciences CenterLubbockTXUSA Department of Neurology Texas Tech University Health Sciences CenterLubbockTXUSA Department of Speech Language and Hearing SciencesTexas Tech University Health Sciences CenterLubbockTXUSA Department of public Health Texas Tech University Health Sciences CenterLubbockTXUSA

The process of neurite outgrowth and branching is a crucial aspect of neuronal development and *** and dendrites,sometimes referred to as neurites,are extensions of a neuron's cellular body that are used to start *** we explored the effects of diethyl(3,4-dihydroxyphenethylamino)(quinolin-4-yl)methylphosphonate(DDQ)on neurite developmental features in HT22 neuronal *** this work,we examined the protective effects of DDQ on neuronal processes and synaptic outgrowth in differentiated HT22cells expressing mutant Tau(mTau)*** investigate DDQ chara cteristics,cell viability,biochemical,molecular,western blotting,and immunocytochemistry were *** outgrowth is evaluated through the segmentation and measurement of neural *** neural processes can be seen and measured with a fluorescence microscope by manually tracing and measuring the length of the neurite *** neuronal processes can be observed and quantified with a fluorescent microscope by manually tracing and measuring the length of the neuronal ***-treated mTau-HT22 cells(HT22 cells transfected with cDNA mutant Tau)were seen to display increased levels of synaptophysin,MAp-2,andβ-***,we confirmed and noted reduced levels of both total and p-Tau,as well as elevated levels of microtubule-associated protein 2,β-tubulin,synaptophysin,vesicular acetylcholine transporter,and the mitochondrial biogenesis protein-pe roxisome prolife rator-activated receptor-gamma coactivator-1α.In mTa u-expressed HT22 neurons,we observed DDQ enhanced the neurite characteristics and improved neurite development through increased synaptic *** findings conclude that mTa u-HT22(Alzheimer's disease)cells treated with DDQ have functional neurite developmental chara *** key finding is that,in mTa u-HT22 cells,DDQ preserves neuronal structure and may even enhance nerve development function with mTa u inhibition.

关键词： diethyl(3 4-dihydroxyphenethylamino)(quinolin-4-yl)methylphosphonate(DDQ) hippocampal neuronal cells HT22 neurite outgrowth neuronal development small molecule