Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 52Citation - Scopus: 54Fractional Caputo Heat Equation Within the Double Laplace Transform(Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; MatematikThe heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transformArticle Citation - WoS: 104Citation - Scopus: 119Fractional Treatment: an Accelerated Mass-Spring System(Editura Acad Romane, 2022) Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; Defterli, Özlem; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H.; MatematikThe aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and derive the classical equations of motion using the Euler-Lagrange equations of integer-order. Furthermore, the generalized Lagrangian is introduced by using non-integer, so-called fractional, derivative operators; then the resulting fractional Euler-Lagrange equations are generated and solved numerically. The obtained results are presented illustratively by using numerical simulations.Article Citation - WoS: 73Citation - Scopus: 98Anomalous Diffusion Models With General Fractional Derivatives Within the Kernels of the Extended Mittag-Leffler Type Functions(Editura Acad Romane, 2017) Yang, Xiao-Jun; Baleanu, Dumitru; Tenreiro Machado, J. A.; Baleanu, Dumitru; Machado, J. A. Tenreiro; MatematikThis paper addresses the new general fractional derivatives (GFDs) involving the kernels of the extended Mittag-Leffler type functions (MLFs). With the aid of the GFDs in the MLF kernels, the mathematical models for the anomalous diffusion of fractional order are analyzed and discussed. The proposed formulations are also used to describe complex phenomena that occur in heat transfer.Article Citation - WoS: 1Citation - Scopus: 1On the Quantitative Weighted Generalization of Jafari Transform(Univ Nis, Fac Sci Math, 2025) Yazici, Serdal; Cekim, Bayram; Jarad, Fahd; Jafari, HosseinIn this paper, a quantitative weighted transform based on the Jafari transform is proposed, and the mathematical foundations of this new transform are investigated. In the first section, some information about Jafari transform and some mathematical tools are reviewed. In the second section, the quantitative weighted Jafari transform is introduced, its existence guaranteed through a theorem, and its fundamental properties are examined. Additionally, transforms of the fractional derivative and fractional integral of a function with respect to a function h and a w-weight are obtained. In the third section, the theoretical findings are applied to solve classical and fractional initial value problems based on a function h and w-weight. In the last section, the results are discussed.Article Citation - Scopus: 1Adapting Integral Transforms To Create Solitary Solutions for Partial Differential Equations Via a New Approach(New York Business Global Llc, 2023) Baleanu, Dumitru; Saadeh, Rania; Qazza, Ahmad; Burqan, AliaaIn this article, a new effective technique is implemented to solve families of nonlinear partial differential equations (NLPDEs). The proposed method combines the double ARA-Sumudu transform with the numerical iterative method to get the exact solutions of NLPDEs. The suc-cessive iterative method was used to find the solution of nonlinear terms of these equations. In order to show the efficiency and applicability of the presented method, some physical applications are analyzed and illustrated, and to defend our results, some numerical examples and figures are discussed.Article Citation - WoS: 33Citation - Scopus: 39An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag-Leffler Kernel(Asme, 2021) Prakasha, D. G.; Baleanu, Dumitru; Veeresha, P.In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method ( q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag-Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.Article Citation - WoS: 16Citation - Scopus: 17A Unifying Computational Framework for Fractional Gross-Pitaevskii Equations(Iop Publishing Ltd, 2021) Baleanu, Dumitru; Veeresha, P.This paper concerns investigating the complex behaviour of the special case of Schrodinger equation called Gross-Pitaevskii (GP) equations using q-homotopy analysis transform method (q-HATM) with fractional order. Based on denticity function and different initial conditions, we consider three different examples to demonstrate the proficiency of q-HATM. We consider different initial conditions for the hired system and the projected method is elegant unification of q-homotopy analysis algorithm and Laplace transform. Further, the physical natures of the achieved results have been captured for change in space, time, homotopy parameter and fractional order in terms of contour and surface plots, and the accuracy is presented with the numerical study. The obtained results conclude that, the hired technique is highly methodical, easy to implement and accurate to examine the behaviour of the nonlinear equations of both fractional and integer order describing allied areas of science.Article Citation - WoS: 45Citation - Scopus: 48Laplace Homotopy Perturbation Method for Burgers Equation With Space- and Time-Fractional Order(Sciendo, 2016) Jafari, H.; Moshokoa, S. P.; Ariyan, V. M.; Baleanu, D.; Johnston, S. J.The fractional Burgers equation describes the physical processes of unidirectional propagation of weakly nonlinear acoustic waves through a gas-filled pipe. The Laplace homotopy perturbation method is discussed to obtain the approximate analytical solution of space-fractional and time-fractional Burgers equations. The method used combines the Laplace transform and the homotopy perturbation method. Numerical results show that the approach is easy to implement and accurate when applied to partial differential equations of fractional orders.Article Citation - WoS: 268Citation - Scopus: 281Caputo-Fabrizio Derivative Applied To Groundwater Flow Within Confined Aquifer(Asce-amer Soc Civil Engineers, 2017) Baleanu, Dumitru; Atangana, AbdonThe model of the movement of subsurface water via the geological formation called aquifer was extended using a newly proposed derivative with fractional order. An alternative derivative to that of Caputo-Fabrizio with fractional order was presented. The relationship between both derivatives was presented. The new equation was solved analytically using some integral transforms. The exact solution is therefore compared to experimental data obtained from the settlement of the University of the Free State in South Africa. The numerical simulation shows the agreement of the experimental data with an analytical solution for some values of fractional order. (C) 2016 American Society of Civil Engineers.