Matematik Bölümü Yayın Koleksiyonu

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

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Author: search.filters.author.Kumar, DevendraWoS Q: search.filters.wosQuartile.Q1

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  • Editorial
  • Article
    Citation - WoS: 22
    Citation - Scopus: 25
    New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain
    (Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran Sooppy
    This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.
  • Article
    An Efficient Algorithm for the Numerical Evaluation of Pseudo Differential Operator With Error Estimation
    (Amer inst Mathematical Sciences-aims, 2022) Pandey, Amit K.; Tripathi, Manoj P.; Singh, Harendra; Rao, Pentyala S.; Kumar, Devendra; Baleanu, D.
    In this paper we introduce an efficient and new numerical algorithm for evaluating a pseudo differential operator. The proposed algorithm is time saving and fruitful. The theoretical as well as numerical error estimation of the algorithm is established, together with its stability analysis. We have provided numerical illustrations and established that the numerical findings echo the analytical findings. The proposed technique has a convergence rate of order three. CPU time of computation is also listed. Trueness of numerical findings are validated using figures.
  • Article
    Citation - WoS: 20
    A Novel Finite Difference Based Numerical Approach for Modified Atangana-Baleanu Caputo Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika
    In this paper, a new approach is presented to investigate the time-fractional advection-dispersion equation that is extensively used to study transport processes. The present modified fractional derivative operator based on Atangana-Baleanu's definition of a derivative in the Caputo sense involves singular and non-local kernels. A numerical approximation of this new modified fractional operator is provided and applied to an advection-dispersion equation. Through Fourier analysis, it has been proved that the proposed scheme is unconditionally stable. Numerical examples are solved that validate the theoretical results presented in this paper and ensure the proficiency of the numerical scheme.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 4
    Novel Numerical Approach for Time Fractional Equations With Nonlocal Condition
    (Springer, 2024) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, Komal
    A numerical method for solving inhomogeneous nonlocal time fractional convection-diffusion-reaction equations with variable coefficients has been developed. The fractional time operator is taken in the sense of the modified operator with the Mittag-Leffler kernel. The numerical method is based on the modified Gauss elimination with Taylor's expansion. Through rigorous analysis, it has been proved that the given method is unconditionally stable and second-order convergent in space and time. The numerical results for three test problems illustrate the efficiency and validity of the theoretical estimates.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    A Higher-Order Approach for Time-Fractional Generalized Burgers' Equation
    (World Scientific Publ Co Pte Ltd, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, Komal
    A fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers' equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann's method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L-2-norm. The scheme's proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.
  • 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: 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.
  • Editorial
    Citation - WoS: 2
    Citation - Scopus: 3
    Editorial Note on the Special Issue: "fractional Calculus Models for the Dynamics of Complex Systems
    (Elsevier, 2021) Kumar, Devendra; Pinto, Carla M. A.; Baleanu, Dumitru; Sweilam, Nasser H.
  • 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.