Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 10 of 21
  • Article
    Citation - WoS: 32
    Citation - Scopus: 38
    On the Analysis of an Analytical Approach for Fractional Caudrey-Dodd Equations
    (Elsevier, 2022) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev
    The principal aim of this paper is to study the approximate solution of nonlinear Caudrey-Dodd-Gibbon equation of fractional order by employing an analytical method. The Caudrey-Dodd-Gibbon equation arises in plasma physics and laser optics. The Caputo derivative is applied to model the physical problem. By applying an effective semi-analytical technique, we attain the approximate solutions without linearization. The uniqueness and the convergence analysis for the applied method are shown. The graphical representation of solutions of fractional Caudrey-Dodd-Gibbon equation demonstrates the applied technique is very efficient to obtain the solutions of such type of fractional order mathematical models. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
  • Article
    Citation - WoS: 15
    Citation - Scopus: 19
    New Aspects of Fractional Bloch Model Associated With Composite Fractional Derivative
    (Edp Sciences S A, 2021) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    This paper studies a fractional Bloch equation pertaining to Hilfer fractional operator. Bloch equation is broadly applied in physics, chemistry, nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and many more. The sumudu transform technique is applied to obtain the analytic solutions for nuclear magnetization M = (M-x, M-y, M-z). The general solution of nuclear magnetization M is shown in the terms of Mittag-Leffler (ML) type function. The influence of order and type of Hilfer fractional operator on nuclear magnetization M is demonstrated in graphical form. The study of Bloch equation with composite fractional derivative reveals the new features of Bloch equation. The discussed fractional Bloch model provides crucial and applicable results to introduce novel information in scientific and technological fields.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 32
    Fractional Order Continuity of a Time Semi-Linear Fractional Diffusion-Wave System
    (Elsevier, 2020) Luu Vu Cam Hoan; Karapinar, Erdal; Singh, Jagdev; Ho Duy Binh; Nguyen Huu Can; Nguyen Duc Phuong; Hoan, Luu Vu Cam; Binh, Ho Duy; Phuong, Nguyen Duc; Can, Nguyen Huu
    In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion about continuity with respect to the fractional derivative order. We find the answer to the question: When the fractional orders get closer, are the corresponding solutions close? To answer this question, we present some depth theories on PDEs and fractional calculus. In addition, we add an example numerical to verify the proposed theory. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
  • 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: 69
    Citation - Scopus: 90
    Analysis of Fractional Model of Guava for Biological Pest Control With Memory Effect
    (Elsevier, 2021) Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    Introduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
  • Article
    Citation - WoS: 46
    Citation - Scopus: 56
    Analysis and Dynamics of Fractional Order Covid-19 Model With Memory Effect
    (Elsevier, 2021) Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Yadav, Supriya
    The present article attempts to examine fractional order Covid-19 model by employing an efficient and powerful analytical scheme termed as q-homotopy analysis Sumudu transform method (q-HASTM). The q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. Liouville-Caputo approach of the fractional operator has been employed. The proposed modelis also examined numerically via generalized Adams-Bashforth-Moulton method. We determined model equilibria and also give their stability analysis by employing next generation matrix and fractional Routh-Hurwitz stability criterion.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 27
    A Hybrid Analytical Algorithm for Thin Film Flow Problem Occurring in Non-Newtonian Fluid Mechanics
    (Elsevier, 2021) Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Sushila
    In this work, we investigate thin film flow of a third grade fluid down a inclined plane. The solution of a nonlinear boundary value problem (BVP) is derived by using an effective well organized computational scheme namely homotopy perturbation Elzaki transform method. Furthermore, this model is also resolved by Elzaki decomposition technique. The outcomes achieved by these two approaches are consistent with each other and because of that this technique may be regarded as an optional and effective scheme for determining results of linear and nonlinear BVP. Moreover, the homotopy perturbation Elzaki transform method leads over the Elzaki decomposition method since the nonlinear problems are solved without utilization of Adomian polynomials. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.
  • Article
    Citation - WoS: 185
    Citation - Scopus: 202
    An Efficient Numerical Method for Fractional Sir Epidemic Model of Infectious Disease by Using Bernstein Wavelets
    (Mdpi, 2020) Ahmadian, Ali; Kumar, Ranbir; Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Salimi, Mehdi; Kumar, Sunil
    In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams-Bashforth-Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams-Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.
  • 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.