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, DevendraPublication Index: search.filters.publicationIndex.PubMed

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  • 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.
  • Article
    Citation - WoS: 71
    Citation - Scopus: 80
    An Efficient Computational Technique for Fractal Vehicular Traffic Flow
    (Mdpi, 2018) Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
  • Article
    Citation - WoS: 110
    Citation - Scopus: 120
    On the Analysis of Chemical Kinetics System Pertaining To a Fractional Derivative With Mittag-Leffler Type Kernel
    (Aip Publishing, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    The pivotal aim of this paper was to analyze a new fractional model of chemical kinetics system related to a newly discovered Atangana-Baleanu derivative with fractional order having non-singular and non-local kernel. The numerical solution is derived by making use of the iterative scheme. The existence of the solution of chemical kinetics system of arbitrary order is examined by implementing the fixed-point theorem. The uniqueness of the special solution of the studied model is shown. The effect of different variables and order of arbitrary ordered derivative on concentrations is demonstrated in tabular and graphical forms. The numerical results for chemical kinetics system pertaining to the newly derivative with fractional order are compared with the chemical kinetics system involving classical derivative. Published by AIP Publishing.