Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Access Right: Closed AccessAuthor: search.filters.author.Singh, Jagdev

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  • Article
    Citation - WoS: 63
    Citation - Scopus: 76
    A Fractional Model of Convective Radial Fins With Temperature-Dependent Thermal Conductivity
    (Editura Acad Romane, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
    The principal purpose of the present article is to examine a fractional model of convective radial fins having constant and temperature-dependent thermal conductivity. In order to solve fractional order energy balance equation, a numerical algorithm namely homotopy analysis transform method is considered. The fin temperature is derived in terms of thermo-geometric fin parameter. Our method is not limited to the use of a small parameter, such as in the standard perturbation technique. The numerical simulation for temperature and fin tip temperature are presented graphically. The results can be used in thermal design to consider radial fins having both constant and temperature-dependent thermal conductivity.
  • Article
    Citation - WoS: 9
    Analytic Study of Allen-Cahn Equation of Fractional Order
    (int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
    The key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.
  • Editorial
  • Article
    Citation - WoS: 8
    Citation - Scopus: 15
    Fractional Dynamics and Analysis of Coupled Schrodinger-Kdv Equation With Caputo-Katugampola Type Memory
    (Asme, 2023) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev
    Fundamental purpose of the current research article is to analyze the behavior of obtained results of time fractional nonlinear coupled Schrodinger-KdV equation, via implementing an effective analytical technique. In this work, Katugampola fractional derivative in Caputo type is used to model the problem. The coupled Schrodinger-KdV equation describes several kinds of wave propagation in plasma physics, like electromagnetic waves, dust-acoustic waves, and Langmuir waves. The fixed point theorem is used to present the existence and uniuness analysis of obtained solution of the discussed model. Numerical simulation and graphical behavior of the model are presented to show the reliability of the implemented analytical technique. A comparative analysis of exact and obtained approximate solutions is also presented.
  • Article
    Citation - WoS: 38
    Citation - Scopus: 44
    Fractional Klein-Gordon Equations With Mittag-Leffler Memory
    (Elsevier, 2020) Prakasha, D. G.; Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Veeresha, P.
    The main objective of the present investigation is to find the solution for the fractional model of Klein-Gordon-Schrodinger system with the aid of q-homotopy analysis transform method (q-HATM). The projected solution procedure is an amalgamation of q-HAM with Laplace transform. More preciously, to elucidate the effectiveness of the projected scheme we illustrate the response of the q-HATM results, and the numerical simulation is offered to guarantee the exactness. Further, the physical behaviour has been presented associated with parameters present the method with respect fractional-order. The present study confirms that, the projected solution procedure is highly methodical and accurate to solve and study the behaviours of the system of differential equations with arbitrary order exemplifying the real word problems.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 52
    Computational Study of Fractional Order Smoking Model
    (Pergamon-elsevier Science Ltd, 2021) Baleanu, Dumitru; Singh, Jagdev; Dutta, Hemen; Singh, Harendra
    Smoking is a very challenging problem the world is facing every day. It contributes to deaths and major health problems to millions of people every year around the world. A lot of work has been devoted to study how to minimize smoking in the society. Here we study non-integer order smoking model using an iterative scheme which is combination of discretization of domain and short memory principle. We will also discuss stability of the proposed model and used iterative scheme. CPU time is listed in tabular to show the efficiency and figures are used to show behaviour of solution in long time. The proposed technique has high accuracy and low computational cost. Using figures fractional time behaviour of solution is also plotted. (C) 2020 Published by Elsevier Ltd.
  • Article
    Citation - WoS: 57
    Citation - Scopus: 72
    An Efficient Computational Approach for Local Fractional Poisson Equation in Fractal Media
    (Wiley, 2021) Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; Singh, Jagdev
    In this article, we analyze local fractional Poisson equation (LFPE) by employing q-homotopy analysis transform method (q-HATM). The PE describes the potential field due to a given charge with the potential field known, one can then calculate gravitational or electrostatic field in fractal domain. It is an elliptic partial differential equations (PDE) that regularly appear in the modeling of the electromagnetic mechanism. In this work, PE is studied in the local fractional operator sense. To handle the LFPE some illustrative example is discussed. The required results are presented to demonstrate the simple and well-organized nature of q-HATM to handle PDE having fractional derivative in local fractional operator sense. The results derived by the discussed technique reveal that the suggested scheme is easy to employ and computationally very accurate. The graphical representation of solution of LFPE yields interesting and better physical consequences of Poisson equation with local fractional derivative.
  • Article
    Citation - WoS: 53
    Citation - Scopus: 58
    An Efficient Computational Technique for Fractional Model of Generalized Hirota-Satsuma Korteweg-De Vries and Coupled Modified Korteweg-De Vries Equations
    (Asme, 2020) Prakasha, D. G.; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Veeresha, P.
    The aim of the present investigation to find the solution for fractional generalized Hirota-Satsuma coupled Korteweg-de-Vries (KdV) and coupled modified KdV (mKdV) equations with the aid of an efficient computational scheme, namely, fractional natural decomposition method (FNDM). The considered fractional models play an important role in studying the propagation of shallow-water waves. Two distinct initial conditions are choosing for each equation to validate and demonstrate the effectiveness of the suggested technique. The simulation in terms of numeric has been demonstrated to assure the proficiency and reliability of the future method. Further, the nature of the solution is captured for different value of the fractional order. The comparison study has been performed to verify the accuracy of the future algorithm. The achieved results illuminate that, the suggested computational method is very effective to investigate the considered fractional-order model.
  • Article
    Citation - WoS: 108
    Citation - Scopus: 122
    A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler Kernel
    (World Scientific Publ Co Pte Ltd, 2020) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    In this paper, we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order. The model is constituted with the group of non-linear differential equations having nutrients, fish and mussel. We have included discrete kind gestational delay of fish. The solution of fish farm model is determined by employing homotopy analysis transforms method (HATM). Existence of and uniqueness of solution are studied through Picard-Lindelof approach. The influence of order of new non-integer order derivative on nutrients, fish and mussel is discussed. The complete study reveals that the outer food supplies manage the behavior of the model. Moreover, to show the outcomes of the study, some numerical results are demonstrated through graphs.
  • Article
    Citation - WoS: 122
    Citation - Scopus: 138
    A New Numerical Algorithm for Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses
    (Springer, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    The principal objective of this study is to present a new numerical scheme based on a combination of q-homotopy analysis approach and Laplace transform approach to examine the Fitzhugh-Nagumo (F-N) equation of fractional order. The F-N equation describes the transmission of nerve impulses. In order to handle the nonlinear terms, the homotopy polynomials are employed. To validate the results derived by employing the used scheme, we study the F-N equation of arbitrary order by using the fractional reduced differential transform scheme. The error analysis of the proposed approach is also discussed. The outcomes are shown through the graphs and tables that elucidate that the used schemes are very fantastic and accurate.