WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 4Citation - Scopus: 4Nonlinear Wave Train in an Inhomogeneous Medium With the Fractional Theory in a Plane Self-Focusing(Amer inst Mathematical Sciences-aims, 2022) Faridi, Waqas Ali; Jhangeer, Adil; Aleem, Maryam; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; Asjad, Muhammad ImranThe aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional beta differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and beta fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and beta-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.Article Citation - WoS: 21Citation - Scopus: 22Dynamics and Numerical Investigations of a Fractional-Order Model of Toxoplasmosis in the Population of Human and Cats(Pergamon-elsevier Science Ltd, 2021) Ali, Nigar; Baleanu, Dumitru; Zafar, Zain Ul AbadinIn this paper an arbitrary order model for Toxoplasmosis ailment in the humanoid and feline is verbalized and explored. The dynamics of this ailment is discovered using an epidemiology type paradigm. We have proposed the fractional order multistage differential transform method for the Toxoplasmosis model. It is employed to analyze and find the elucidation for the model, and the numerical simulations have been conducted in order to study the effectiveness of the technique. The suggested algorithm can be considered as a fractional extension of the well know method known as Multistage Differential Transform Method. The sensitivity analysis of the strictures of the specimen is discussed. The numeric imitations of the projected non-integer specimens are conceded out to illustrate different dynamics of the model, which depend on R-0. (C) 2021 Elsevier Ltd. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 5Comparison Principles of Fractional Differential Equations With Non-Local Derivative and Their Applications(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Al-Refai, MohammedIn this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.Article Citation - WoS: 11Citation - Scopus: 13Fractional Hamilton's Equations of Motion in Fractional Time(de Gruyter Poland Sp Z O O, 2007) Baleanu, Dumitru; Rabei, Eqab M.; Muslih, Sami I.The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton's equations are obtained and two examples are investigated in detail. (C) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.Article Citation - WoS: 11Citation - Scopus: 11Steady Periodic Response for a Vibration System With Distributed Order Derivatives To Periodic Excitation(Sage Publications Ltd, 2018) Baleanu, Dumitru; Duan, Jun-ShengSteady-state periodic responses for a vibration system with distributed order derivatives are investigated, where the fractional derivative operator -infinity D-t(beta) is utilized. The response to complex harmonic excitation is derived and the amplitude-frequency and phase-frequency relations are obtained. For a periodic excitation, we decompose it into the Fourier series, and then make use of the principle of superposition and the results of harmonic excitations to obtain the response. Finally, we examine three numerical examples by using the proposed method.Article Citation - WoS: 198Citation - Scopus: 213A New Fractional Exothermic Reactions Model Having Constant Heat Source in Porous Media With Power, Exponential and Mittag-Leffler Laws(Pergamon-elsevier Science Ltd, 2019) Singh, Jagdev; Tanwar, Kumud; Baleanu, Dumitru; Kumar, DevendraThe present article deals with the exothermic reactions model having constant heat source in the porous media with strong memory effects. The Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional operators are used to induce memory effects in the mathematical modeling of exothermic reactions. The patterns of heat flow profiles are very essential for heat transfer in every kind of the thermal insulation. In the present investigation, we focus on the driving force problem due to the fact that temperature gradient is assumed. The mathematical equation of the problem is confined in a fractional energy balance equation (FEBE), which furnishes the temperature portrayal in conduction state having uniform heat source on steady state. The fractional Laplace decomposition technique is utilized to obtain the numerical solution of the corresponding FEBE describing the exothermic reactions. Some numerical results for the fractional exothermic reactions model are presented through graphs and tables. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 74Citation - Scopus: 86Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations(Mdpi, 2019) Baleanu, Dumitru; Waheed, Asif; Khan, Mansoor Shaukat; Affan, Hira; Javeed, ShumailaThe analysis of Homotopy PerturbationMethod (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for alpha = 1, is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.Article Citation - WoS: 44Citation - Scopus: 53Some New Fractional-Calculus Connections Between Mittag-Leffler Functions(Mdpi, 2019) Fernandez, Arran; Baleanu, Dumitru; Srivastava, Hari M.We consider the well-known Mittag-Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag-Leffler function as a fractional derivative of the two-parameter Mittag-Leffler function, which is in turn a fractional integral of the one-parameter Mittag-Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag-Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.Article Citation - WoS: 13Citation - Scopus: 14A Generalisation of the Malgrange-Ehrenpreis Theorem To Find Fundamental Solutions To Fractional Pdes(Univ Szeged, Bolyai institute, 2017) Fernandez, Arran; Baleanu, DumitruWe present and prove a new generalisation of the Malgrange-Ehrenpreis theorem to fractional partial differential equations, which can be used to construct fundamental solutions to all partial differential operators of rational order and many of arbitrary real order. We demonstrate with some examples and mention a few possible applications.Article Citation - WoS: 33Citation - Scopus: 40Higher Order Fractional Variational Optimal Control Problems With Delayed Arguments(Elsevier Science inc, 2012) Jarad, Fahd; Abdeljawad (Maraaba), Thabet; Baleanu, Dumitru; Abdeljawad , ThabetThis article deals with higher order Caputo fractional variational problems in the presence of delay in the state variables and their integer higher order derivatives. (C) 2012 Elsevier Inc. All rights reserved.