WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
14 results
Search Results
Article Citation - WoS: 1Citation - Scopus: 1Left-Definite Fractional Hamiltonian Systems: Titchmarsh-Weyl Theory(Pergamon-Elsevier Science Ltd, 2025) Ugurlu, EkinHamiltonian systems are useful when formally symmetric boundary value problems generated by ordinary derivatives are considered. However, if the ordinary derivatives are changed by non-integer-order (fractional) derivatives, it is not easy to investigate the corresponding problems. In this paper, we introduce a systematic approach to dealing with fractional boundary value problems by constructing a fractional Hamiltonian system. In particular, we consider a left-definite system, and we construct nested-circles theory (Weyl theory) for this system of equations. Using the Titchmarsh-Weyl function, we prove that at least r-solutions of the 2r-dimensional system of equations should be Dirichlet-integrable on a given interval.Article Citation - WoS: 5Citation - Scopus: 5On Some Fractional Operators Generated From Abel's Formula(Tubitak Scientific & Technological Research Council Turkey, 2022) Ugurlu, EkinThis work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup property for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.Article Citation - WoS: 26Citation - Scopus: 32On a More General Fractional Integration by Parts Formulae and Applications(Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, AbdonThe integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.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: 42Citation - Scopus: 49An Efficient Technique for Solving the Space-Time Fractional Reaction-Diffusion Equation in Porous Media(Elsevier, 2020) Kumar, Sachin; Gomez-Aguilar, J. F.; Baleanu, D.; Pandey, PrashantIn this paper, we obtained the approximate numerical solution of space-time fractional-order reaction-diffusion equation using an efficient technique homotopy perturbation technique using Laplace transform method with fractional-order derivatives in Caputo sense. The solution obtained is very useful and significant to analyze the many physical phenomenons. The present technique demonstrates the coupling of the homotopy perturbation technique and Laplace transform using He's polynomials for finding the numerical solution of various non-linear fractional complex models. The salient features of the present work are the graphical presentations of the approximate solution of the considered porous media equation for different particular cases and reflecting the presence of reaction terms presented in the equation on the physical behavior of the solute profile for various particular cases.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: 15Citation - Scopus: 17Fractional Dynamics of an Erbium-Doped Fiber Laser Model(Springer, 2019) Saad, K. M.; Baleanu, D.; Gomez-Aguilar, J. F.In this paper we investigate the model of the time-fractional dynamics of an erbium-doped fiber laser model (TFDEFL) with Liouville-Caputo (LC), Caputo-Fabrizio-Caputo (CFC) and Atangana-Baleanu-Caputo (ABC) time-fractional derivatives. We employ the homotopy analysis transform method (HATM) to calculate approximate solutions for the TFDEFL model. This method gives the solution in the form of a rapidly convergent series that can ensure the convergence in solving the resultant series. We study the convergence analysis of HATM by computing the interval of convergence through the h-curves, the residual error function and the average residual error, respectively. We also show the effectiveness and accuracy of this method by comparing the approximate solutions based upon the LC, CFC and ABC time-fractional derivatives.Article Citation - WoS: 22Citation - Scopus: 31Hamilton-Jacobi and Fractional Like Action With Time Scaling(Springer, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.; Herzallah, Mohamed A. E.This paper represents the Hamilton-Jacobi formulation for fractional variational problem with fractional like action written as an integration over a time scaling parameter. Also we developed the fractional Hamiltonian formulation for the fractional like action. In all the given calculations, the most popular Riemann-Liouville (RL) and Caputo fractional derivatives are employed. An example illustrates our approach.Article Citation - WoS: 9Citation - Scopus: 8Fractional Time Action and Perturbed Gravity(World Scientific Publ Co Pte Ltd, 2011) Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab; Sadallah, MadhatIn this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, by applying the variational principle to this new fractional action, we obtained the modified Euler-Lagrange equations of motion in any fractional time of order 0 < alpha <= 1. Two examples are investigated in detail.