WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 18Citation - Scopus: 31Solving Fractional Integro-Differential Equations by Aboodh Transform(int Scientific Research Publications, 2024) Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru; Raghavendran, PrabakaranThis study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, which is generalized. The method presented here is based mostly on certain general theorems on particular solutions of FIDEs using the Aboodh transform and binomial series extension coefficients. We additionally demonstrate techniques to solve FIDEs.Article Citation - WoS: 3Citation - Scopus: 4Numerical Analysis of Fractional Order Discrete Bloch Equa-Tions(int Scientific Research Publications, 2024) Santra, Shyam Sundar; Jayanathan, Leo Amalraj; Baleanu, Dumitru; Murugesan, MeganathanBy defining a new kind of h-extorial function with constant coefficient, this research seeks to solve discrete fractional Bloch equations. By using an extorial function of the Mittag-Leffler type, we are able to discover the general solutions for the magnetization's Bx, By, and Bz components. These findings demonstrate the innovative method of fractional order Bloch equations. In addition, we offer a graphical representation of our results.(c) 2024 All rights reserved.Article Citation - WoS: 35Citation - Scopus: 35Optical Solitons for Conformable Space-Time Fractional Nonlinear Model(int Scientific Research Publications, 2022) Ullah, Naeem; Rehman, Hamood Ur; Baleanu, Dumitru; Asjad, Muhammad ImranIn search of the exact solutions of nonlinear partial differential equations in solitons form has become most popular to understand the internal features of physical phenomena. In this paper, we discovered various type of solitons solutions for the conformable space-time nonlinear Schrodinger equation (CSTNLSE) with Kerr law nonlinearity. To seek such solutions, we applied two proposed methods which are Sardar-subequation method and new extended hyperbolic function method. In this way several types of solitons obtained for example bright, dark, periodic singular, combined dark-bright, singular, and combined singular solitons. Some of the acquired solutions are interpreted graphically. These solutions are specific, novel, correct and may be beneficial for edifying precise nonlinear physical phenomena in nonlinear dynamical schemes. It is revealed that the proposed methods offer a straightforward and mathematical tool for solving nonlinear conformable space-time nonlinear Schrodinger equation. These results support in attaining nonlinear optical fibers in the future.Article Citation - WoS: 2Some New Exact Solutions for a Generalized Variable Coeffi- Cients Kdv Equation(int Scientific Research Publications, 2023) Kader, Abass H. Abdel; Latif, Mohamed S. Abdel; Baleanu, Dumitru; El Sonbaty, Amr; Rajagopalan, R.In this paper, the variable coefficients KdV equation with general power nonlinearities is proposed. Firstly, it is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to transform the obtained constant coefficients generalized KdV equation into a generalized ordinary differential equation. We give a classification for the obtained generalized ordinary differential equation using a suitable integrating factor. Some new solutions are obtained for the generalized KdV equation with constant coefficients. All the obtained solutions in this paper for the variable coefficients KdV equation with general power nonlinearities are new.Article Citation - WoS: 2Citation - Scopus: 3On New Traveling Wave Solutions of Potential Kdv and (3+1)-Dimensional Burgers Equations(int Scientific Research Publications, 2016) Inan, Ibrahim E.; Ugurlu, Yavuz; Inc, Mustafa; Baleanu, Dumitru; Tchiera, Fairouz; Tchier, FairouzThis paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables (G'/G, 1/G) expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena. (C) 2016 All rights reserved.Article Citation - WoS: 68Citation - Scopus: 80Application of Shehu Transform To Atangana-Baleanu Derivatives(int Scientific Research Publications, 2020) Baleanu, Dumitru; Belgacem, Rachid; Bokhari, AhmedRecently, Shehu Maitama and Weidong Zhao proposed a new integral transform, namely, Shehu transform, which generalizes both the Sumudu and Laplace integral transforms. In this paper, we present new further properties of this transform. We apply this transformation to Atangana-Baleanu derivatives in Caputo and in Riemann-Liouville senses to solve some fractional differential equations.Article Citation - WoS: 32A New Numerical Technique for Local Fractional Diffusion Equation in Fractal Heat Transfer(int Scientific Research Publications, 2016) Tenreiro Machado, J. A.; Baleanu, Dumitru; Gao, Feng; Yang, Xiao-JunIn this paper, a new numerical approach, embedding the differential transform (DT) and Laplace transform (LT), is firstly proposed. It is considered in the local fractional derivative operator for obtaining the non-differential solution for diffusion equation in fractal heat transfer. (C) 2016 All rights reserved.Article Citation - WoS: 59Residual Power Series Method for Time-Fractional Schrodinger Equations(int Scientific Research Publications, 2016) Kumar, Amit; Kumar, Sunil; Baleanu, Dumitru; Yang, Xiao-Jun; Zhang, YuIn this paper, the residual power series method (RPSM) is effectively applied to find the exact solutions of fractional-order time dependent Schrodinger equations. The competency of the method is examined by applying it to the several numerical examples. Mainly, we find that our solutions obtained by the proposed method are completely compatible with the solutions available in the literature. The obtained results interpret that the proposed method is very effective and simple for handling different types of fractional differential equations (FDEs). (C) 2016 All rights reserved.Article Citation - WoS: 27Citation - Scopus: 50Approximate Analytical Solutions of Goursat Problem Within Local Fractional Operators(int Scientific Research Publications, 2016) Jassim, Hassan Kamil; Al Qurashi, Maysaa; Baleanu, DumitruThe local fractional differential transform method (LFDTM) and local fractional decomposition method (LFDM) are applied to implement the homogeneous and nonhomogeneous Goursat problem involving local fractional derivative operators. The approximate analytical solution of this problem is calculated in form of a series with easily computable components. Examples are studied in order to show the accuracy and reliability of presented methods. We demonstrate that the two approaches are very effective and convenient for finding the analytical solutions of partial differential equations with local fractional derivative operators. (C) 2016 All rights reserved.Article Citation - WoS: 6Citation - Scopus: 7On Generalized Space of Quaternions and Its Application To a Class of Mellin Transforms(int Scientific Research Publications, 2016) Baleanu, Dumitru; Al-Omari, Shrideh Khalaf QasemThe Mellin integral transform is an important tool in mathematics and is closely related to Fourier and bi-lateral Laplace transforms. In this article we aim to investigate the Mellin transform in a class of quaternions which are coordinates for rotations and orientations. We consider a set of quaternions as a set of generalized functions. Then we provide a new definition of the cited Mellin integral on the provided set of quaternions. The attributive Mellin integral is one-to-one, onto and continuous in the quaternion spaces. Further properties of the discussed integral are given on a quaternion context. (C) 2016 All rights reserved.