WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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: 2Citation - Scopus: 2Fractional Evolution Equation With Cauchy Data in L<sup>p</Sup> Spaces(Springer, 2022) Baleanu, Dumitru; Agarwal, Ravi P.; Le Dinh Long; Nguyen Duc Phuong; Long, Le Dinh; Phuong, Nguyen DucIn this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in L-2 and H-s,H- However, there have not been any papers dealing with this problem with observed data in L-p with p not equal 2. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in L-p. To our knowledge, L-p evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.Article Citation - WoS: 4Citation - Scopus: 4Continuity Result on the Order of a Nonlinear Fractional Pseudo-Parabolic Equation With Caputo Derivative(Mdpi, 2021) Hoang, Luc Nguyen; Baleanu, Dumitru; Van, Ho Thi Kim; Binh, Ho DuyIn this paper, we consider a problem of continuity fractional-order for pseudo-parabolic equations with the fractional derivative of Caputo. Here, we investigate the stability of the problem with respect to derivative parameters and initial data. We also show that u(omega ') -> u(omega) in an appropriate sense as omega '-> omega, where omega is the fractional order. Moreover, to test the continuity fractional-order, we present several numerical examples to illustrate this property.Article Citation - WoS: 25Citation - Scopus: 37A Solution of the Fractional Differential Equations in the Setting of B-Metric Space(Vasyl Stefanyk Precarpathian Natl Univ, 2021) Afshari, H.; Karapinar, E.In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems {D(c)(mu)w(sigma) +/- D(c)(nu)w(sigma) = h(sigma, w(sigma)), sigma is an element of J, 0 < nu < mu < 1, w(0) = w(0), where D-mu, D-nu is the Caputo derivative of order mu, nu, respectively and h: J x R -> R is continuous. The results are well demonstrated with the aid of exciting examples.Article Citation - WoS: 4Citation - Scopus: 5A New Analytical Method To Simulate the Mutual Impact of Space-Time Memory Indices Embedded in (1(de Gruyter Poland Sp Z O O, 2022) Jaradat, Imad; Alquran, Marwan; Baleanu, Dumitru; Makhadmih, MohammadIn the present article, we geometrically and analytically examine the mutual impact of space-time Caputo derivatives embedded in (1 + 2)-physical models. This has been accomplished by integrating the residual power series method (RPSM) with a new trivariate fractional power series representation that encompasses spatial and temporal Caputo derivative parameters. Theoretically, some results regarding the convergence and the error for the proposed adaptation have been established by virtue of the Riemann-Liouville fractional integral. Practically, the embedding of Schrodinger, telegraph, and Burgers' equations into higher fractional space has been considered, and their solutions furnished by means of a rapidly convergent series that has ultimately a closed-form fractional function. The graphical analysis of the obtained solutions has shown that the solutions possess a homotopy mapping characteristic, in a topological sense, to reach the integer case solution where the Caputo derivative parameters behave similarly to the homotopy parameters. Altogether, the proposed technique exhibits a high accuracy and high rate of convergence.Article Citation - WoS: 7Citation - Scopus: 7A Decomposition Algorithm Coupled With Operational Matrices Approach With Applications To Fractional Differential Equations(Vinca inst Nuclear Sci, 2021) Alam, Md Nur; Baleanu, Dumitru; Zaidi, Danish; Talib, ImranIn this article, we solve numerically the linear and non-linear fractional initial value problems of multiple orders by developing a numerical method that is based on the decomposition algorithm coupled with the operational matrices approach. By means of this, the fractional initial value problems of multiple orders are decomposed into a system of fractional initial value problems which are then solved by using the operational matrices approach. The efficiency and advantage of the developed numerical method are highlighted by comparing the results obtained otherwise in the literature. The construction of the new derivative operational matrix of fractional legendre function vectors in the Caputo sense is also a part of this research. As applications, we solve several fractional initial value problems of multiple orders. The numerical results are displayed in tables and plots.Article Citation - WoS: 68Citation - Scopus: 74On Continuity of the Fractional Derivative of the Time-Fractional Semilinear Pseudo-Parabolic Systems(Springer, 2021) Ho Duy Binh; Nguyen Hoang Luc; Nguyen Huu Can; Karapinar, Erdal; Binh, Ho Duy; Luc, Nguyen Hoang; Can, Nguyen HuuIn this work, we study an initial value problem for a system of nonlinear parabolic pseudo equations with Caputo fractional derivative. Here, we discuss the continuity which is related to a fractional order derivative. To overcome some of the difficulties of this problem, we need to evaluate the relevant quantities of the Mittag-Leffler function by constants independent of the derivative order. Moreover, we present an example to illustrate the theory.Article Citation - WoS: 16Citation - Scopus: 19Finite-Time Stability of Linear Stochastic Fractional-Order Systems With Time Delay(Springer, 2021) Ben Makhlouf, Abdellatif; Baleanu, Dumitru; Rhaima, Mohamed; Mchiri, LassaadThis paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for alpha is an element of (1/2, 1). Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.Article Citation - WoS: 17Citation - Scopus: 17Yficitious Time Integration Method for Solving the Time Fractional Gas Dynamics Equation(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Baleanu, Dumitru; Moshokoa, Seithuti Philemon; Partohaghighi, MohammadIn this work a poweful approach is presented to solve the time-fractional gas dynamics equation. In fact, we use a fictitious time variable y to convert the dependent variable w(x, t) into a new one with one more dimension. Then by taking a initial guess and implementing the group preserving scheme we solve the problem. Finally four examples are solved to illustrate the power of the offered method.Article Citation - WoS: 11Citation - Scopus: 17Bivariate Chebyshev Polynomials of the Fifth Kind for Variable-Order Time-Fractional Partial Integro-Differential Equations With Weakly Singular Kernel(Springer, 2021) Hosseini, Kamyar; Baleanu, Dumitru; Ahmadian, Ali; Salahshour, Soheil; Sadri, KhadijehThe shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the numerical solution of the problem under study. The suggested method changes solving the VTFWSPIDE into the solution of a system of linear algebraic equations. Error bounds of the approximate solutions are obtained, and the application of the proposed scheme is examined on five problems. The results confirm the applicability and high accuracy of the method for the numerical solution of fractional singular partial integro-differential equations.