Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 1Finite Bivariate Biorthogonal I-Konhauser Polynomials(Elsevier, 2026) Lekesiz, Esra Guldogan; Cekim, Bayram; Ozarslan, Mehmet Ali; Güldoğan Lekesi̇z, EsraIn the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval's identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.Article Citation - WoS: 1A New Formulation and Analytical Applications of Fractional Operators(World Scientific Publ Co Pte Ltd, 2024) Mehmood, Ahsan; Samraiz, Muhammad; Liu, Zhi-Guo; Baleanu, Dumitru; Vivas-Cortez, MiguelThis research paper introduces a novel formulation of the modified Atangana-Baleanu (AB) Fractional Operators (FrOs). The paper begins by discussing the boundedness of the novel fractional derivative operator. Some fractional differential equations corresponding to different choices of functions as well as comparative graphical representations of a function and its derivative are provided. Furthermore, the paper investigates the generalized Laplace transform for this newly introduced operator. By employing the generalized Laplace transform, a wide range of fractional differential equations can be effectively solved. Additionally, the paper establishes the corresponding form of the AB Caputo fractional integral operator, examines its boundedness and obtains its Laplace transform. It is worth noting that the FrOs previously documented in the existing literature can be derived as special cases of these recently explored FrOs.Article Citation - WoS: 1Citation - Scopus: 1Heat Transfer of Mhd Oldroyd-B Fluid With Ramped Wall Velocity and Temperature in View of Local and Nonlocal Differential Operators(World Scientific Publ Co Pte Ltd, 2022) Riaz, Muhammad Bilal; Jarad, Fahd; Asgir, Maryam; Zafar, Azhar AliThe theoretical study focuses on the examination of the convective flow of Oldroyd-B fluid with ramped wall velocity and temperature. The fluid is confined on an extended, unbounded vertical plate saturated within the permeable medium. To depict the fluid flow, the coupled partial differential equations are settled by using the Caputo (C) and Caputo Fabrizio (CF) differential time derivatives. The mathematical analysis of the fractionalized models of fluid flow is performed by Laplace transform (LT). The complexity of temperature and velocity profile is explored by numerical inversion algorithms of Stehfest and Tzou. The fractionalized solutions of the temperature and velocity profile have been traced out under fractional and other different parameters considered. The physical impacts of associated parameters are elucidated with the assistance of the graph using the software MATHCAD 15. We noticed the significant influence of the fractional parameter (memory effects) and other parameters on the dynamics of the fluid flow. Shear stress at the wall and Nusselt number also are considered. It's brought into notice the fractional-order model (CF) is the best fit in describing the memory effects in comparison to the C model. An analysis of the comparison between the solution of velocity and temperature profile for ramped wall temperature and velocity and constant wall temperature and velocity is also performed.Article Citation - WoS: 6Citation - Scopus: 10An Efficient Hybrid Computational Technique for the Time Dependent Lane-Emden Equation of Arbitrary Order(Elsevier, 2022) Prakash, Amit; Baleanu, Dumitru; Goyal, ManishThe study of dynamic behaviour of nonlinear models that arise in ocean engineering play a vital role in our daily life. There are many examples of ocean water waves which are nonlinear in nature. In shallow water, the linearization of the equations imposes severe conditions on wave amplitude than it does in deep water, and the strong nonlinear effects are observed. In this paper, q-homotopy analysis Laplace transform scheme is used to inspect time dependent nonlinear Lane-Emden type equation of arbitrary order. It offers the solution in a fast converging series. The uniqueness and convergence analysis of the considered model is presented. The given examples confirm the competency as well as accuracy of the presented scheme. The behavior of obtained solution for distinct orders of fractional derivative is discussed through graphs. The auxiliary parameter h over bar offers a suitable mode of handling the region of convergence. The outcomes reveal that the q-HATM is attractive, reliable, efficient and very effective. (c) 2021 Shanghai Jiaotong University. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )Article Citation - WoS: 17Citation - Scopus: 17The Analytical Analysis of Nonlinear Fractional-Order Dynamical Models(Amer inst Mathematical Sciences-aims, 2021) Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; Xu, JiabinThe present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.Article The analytical analysis of nonlinear fractional-order dynamical models(Amer Inst Mathematical Sciences-AIMS, 2021) Xu, Jiabin; Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, DumitruThe present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.Article Citation - WoS: 3Citation - Scopus: 4Investigation of Covid-19 Mathematical Model Under Fractional Order Derivative(Edp Sciences S A, 2021) Arfan, Muhammad; Deebani, Wejdan; Shutaywi, Meshal; Baleanu, Dumitru; Shah, KamalThe given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus COVID-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results.Article Citation - WoS: 38Citation - Scopus: 44Fractional Klein-Gordon Equations With Mittag-Leffler Memory(Elsevier, 2020) Prakasha, D. G.; Singh, Jagdev; Kumar, Devendra; Baleanu, Dumitru; Veeresha, P.The main objective of the present investigation is to find the solution for the fractional model of Klein-Gordon-Schrodinger system with the aid of q-homotopy analysis transform method (q-HATM). The projected solution procedure is an amalgamation of q-HAM with Laplace transform. More preciously, to elucidate the effectiveness of the projected scheme we illustrate the response of the q-HATM results, and the numerical simulation is offered to guarantee the exactness. Further, the physical behaviour has been presented associated with parameters present the method with respect fractional-order. The present study confirms that, the projected solution procedure is highly methodical and accurate to solve and study the behaviours of the system of differential equations with arbitrary order exemplifying the real word problems.Article Citation - WoS: 14Citation - Scopus: 33Exact Solutions for Thermomagetized Unsteady Non-Singularized Jeffrey Fluid: Effects of Ramped Velocity, Concentration With Newtonian Heating(Elsevier, 2021) Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; Aziz-Ur-RehmanThe classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results.Article Exact solutions for thermomagetized unsteady non-singularized jeffrey fluid: Effects of ramped velocity, concentration with newtonian heating(Elsevier, 2021) Aziz-Ur, Rehman; Riaz, Muhammad Bilal; Awrejcewicz, Jan; Baleanu, Dumitru; Aziz-ur-rehman,The classical calculus due to the fact that it assumed as the instant rate of change of the output, when the input level changes. Therefore it is not able to include the previous state of the system called memory effect. But in the Fractional Calculus (FC), the rate of change is affected by all points of the considered interval, so it is able to incorporate the previous history/memory effects of any system. Due to the importance of this effect we used the modern concept of the Caputo-Fabrizio fractional derivative on the considered Jeffrey fluid model. In this paper the effect of Newtonian heating, concentration and velocity on unsteady MHD free convective flow of Jeffrey fluid over long vertical an infinite ramped wall nested in porous material are discussed. Exact analytical solutions are derived via Laplace transformation technique for principal equations of energy, concentration and ramped velocity. The prime features of various coherent parameters are deliberated and illuminated with the aid of plotted graphs. A comparative study to show the significance of fractional order model with an integer order model is accomplished. The fractional order model is found to be the best choice for explaining the memory effect of the considered problem. It is identified that temperature distribution, concentration and ramped velocity profiles for fractional model are converges to an ordinary model when fractional parameter tends to integer order, which shows that fractional model is more appropriate to explicate experimental results. © 2021