Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 63Citation - Scopus: 76A Fractional Model of Convective Radial Fins With Temperature-Dependent Thermal Conductivity(Editura Acad Romane, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; MatematikThe 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: 12Citation - Scopus: 21Generalized Invexity and Duality in Multiobjective Variational Problems Involving Non-Singular Fractional Derivative(de Gruyter Poland Sp Z O O, 2022) Kumar, Devendra; Alshehri, Hashim M.; Singh, Jagdev; Baleanu, Dumitru; Dubey, Ved PrakashIn this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo-Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.Article Citation - WoS: 8Citation - Scopus: 9Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes(Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika; Reetika, ChawlaIn the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.Article Citation - WoS: 57Citation - Scopus: 72An 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, JagdevIn 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: 53Citation - Scopus: 58An 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: 201Citation - Scopus: 209Analysis of Regularized Long-Wave Equation Associated With a New Fractional Operator With Mittag-Leffler Type Kernel(Elsevier, 2018) Singh, Jagdev; Baleanu, Dumitru; Sushila; Kumar, DevendraIn this work, we aim to present a new fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana Baleanu fractional derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 100Citation - Scopus: 122A New Analysis of the Fornberg-Whitham Equation Pertaining To a Fractional Derivative With Mittag-Leffler Kernel(Springer Heidelberg, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, DevendraThe mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.Article Citation - WoS: 102Citation - Scopus: 119Analysis of a Fractional Model of the Ambartsumian Equation(Springer Heidelberg, 2018) Singh, Jagdev; Baleanu, Dumitru; Rathore, Sushila; Kumar, DevendraThe prime target of this work is to investigate a fractional model of the Ambartsumian equation. This equation is very useful to describe the surface brightness of the Milky Way. The Ambartsumian equation of fractional order is solved with the aid of the HATM. The solution is presented in terms of the power series, which is convergent for all real values of variables and parameters. The outcomes drawn with the help of the HATM are presented in the form of graphs.Editorial Citation - WoS: 85Citation - Scopus: 91Editorial: Fractional Calculus and Its Applications in Physics(Frontiers Media Sa, 2019) Baleanu, Dumitru; Kumar, DevendraArticle Citation - WoS: 71Citation - Scopus: 80An Efficient Computational Technique for Fractal Vehicular Traffic Flow(Mdpi, 2018) Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; Kumar, DevendraIn 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.