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| 1 | Analysis of Lakes pollution model with Mittag-Leffler kernel显示文摘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 model.The 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 hypothesis.More 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 algorithm.Further,for the different fractional-order and parameters offered by the considered method,the physical natures have been apprehended.The 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. | D.G.Prakasha P.Veeresha | 2020 | Journal of Ocean Engineering and Science2020，5，4： | 2 |
| 2 | Solution for fractional potential KdV and Benjamin equations using the novel technique显示文摘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 investigation.The projected solution procedure manipulates and controls the obtained results in a large admissible domain.Further,it offers a simple algorithm to adjust the convergence province of the obtained solution.To 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 tables.Comparison 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. | P.Veeresha D.G.Prakasha N.Magesh A.John Christopher Deepak Umrao Sarwe | 2021 | Journal of Ocean Engineering and Science2021，6，3： | 2 |
| 3 | Fractional approach for mathematical model of phytoplankton-toxic phytoplankton-zooplankton system with Mittag-Leffler kernel显示文摘The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy analysis transform method(q-HATM)is discussed.The 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 phytoplankton.The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana-Baleanu(AB)operator.The equilibrium points and stability have been discussed with the assistance of the Routh-Hurwitz rule in this work within the frame of generalized calculus.The 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 system.Further,the physical nature of the achieved solution has been captured for fractional order,external force and diverse mass.The 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. | P.Veeresha Lanre Akinyemi | 2023 | International Journal of Biomathematics2023，16，3： | 1 |
| 4 | An efficient technique for two-dimensional fractional order biological population model显示文摘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 efficiency.The nature of FNDM solution has been captured for distinct arbitrary order.In order to illustrate the proficiency and reliability of the considered scheme,the numerical simulation has been presented.The 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. | P.Veeresha D.G.Prakasha | 2020 | International Journal of Modeling, Simulation, and Scientific Computing2020，11，1： | 0 |
| 5 | Regarding Deeper Properties of the Fractional Order Kundu-Eckhaus Equation and Massive Thirring Model显示文摘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 model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The 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. | Yaya Wang P.Veeresha D.G.Prakasha Haci Mehmet Baskonus Wei Gao | 2022 | Computer Modeling in Engineering & Sciences2022，，12： | 0 |
| 6 | Regarding on the Fractional Mathematical Model of Tumour Invasion and Metastasis显示文摘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 operator.The 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 cells.The 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 study.By using the fixed point theory,existence and uniqueness are demonstrated.To validate and present the effectiveness of the considered algorithm,we analyzed the considered system in terms of fractional order with time and space.The error analysis of the considered scheme is illustrated.The variations with small change time with respect to achieved results are effectively captured in plots.The 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. | P.Veeresha Esin Ilhan D.G.Prakasha Haci Mehmet Baskonus Wei Gao | 2021 | Computer Modeling in Engineering & Sciences2021，，6： | 0 |
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