Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Baleanu, DumitruSubject: search.filters.subject.Fractional Differential Equations

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Now showing 1 - 10 of 26
  • Article
    Citation - Scopus: 4
    On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay
    (Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; Matematik
    We prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.
  • Article
    Citation - Scopus: 61
    Solving Multi-Term Orders Fractional Differential Equations by Operational Matrices of Bps With Convergence Analysis
    (2013) Rostamy, D.; Baleanu, Dumitru; Alipour, M.; Jafari, H.; Baleanu, D.; Matematik
    In this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity and applicability of this method.
  • Article
    Citation - WoS: 65
    Citation - Scopus: 65
    Solutions of the Telegraph Equations Using a Fractional Calculus Approach
    (Editura Acad Romane, 2014) Gomez Aguilar, Jose Francisco; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    In this paper, the fractional differential equation for the transmission line without losses in terms of the fractional time derivatives of the Caputo type is considered. In order to keep the physical meaning of the governing parameters, new parameters a and a were introduced. These parameters characterize the existence of the fractional components in the system. A relation between these parameters is also reported. Fractional differential equations are examined with both temporal and spatial fractional derivatives. We show a few illustrative examples when the wave periodicity is broken in either temporal or spatial variables. Finally, we present the output of numerical simulations that were performed with both temporal and spatial fractional derivatives.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 10
    Analytical Treatments To Systems of Fractional Differential Equations With Modified Atangana-Baleanu Derivative
    (World Scientific Publ Co Pte Ltd, 2023) Syam, Muhammed I.; Baleanu, Dumitru; Al-Refai, Mohammed
    The solutions of systems of fractional differential equations depend on the type of the fractional derivative used in the system. In this paper, we present in closed forms the solutions of linear systems involving the modified Atangana-Baleanu derivative that has been introduced recently. For the nonlinear systems, we implement a numerical scheme based on the collocation method to obtain approximate solutions. The applicability of the results is tested through several examples. We emphasize here that certain systems with the Atangana-Baleanu derivative admit no solutions which is not the case with the modified derivative.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 36
    Shifted Ultraspherical Pseudo-Galerkin Method for Approximating the Solutions of Some Types of Ordinary Fractional Problems
    (Springer, 2021) Mahmoud, Doha; Baleanu, Dumitru; El-kady, Mamdouh; Abdelhakem, Mohamed
    In this work, a technique for finding approximate solutions for ordinary fraction differential equations (OFDEs) of any order has been proposed. The method is a hybrid between Galerkin and collocation methods. Also, this method can be extended to approximate fractional integro-differential equations (FIDEs) and fractional optimal control problems (FOCPs). The spatial approximations with their derivatives are based on shifted ultraspherical polynomials (SUPs). Modified Galerkin spectral method has been used to create direct approximate solutions of linear/nonlinear ordinary fractional differential equations, a system of ordinary fraction differential equations, fractional integro-differential equations, or fractional optimal control problems. The aim is to transform those problems into a system of algebraic equations. That system will be efficiently solved by any solver. Three spaces of collocation nodes have been used through that transformation. Finally, numerical examples show the accuracy and efficiency of the investigated method.
  • Article
    Citation - WoS: 114
    Citation - Scopus: 104
    Fractional Calculus in the Sky
    (Springer, 2021) Agarwal, Ravi P.; Baleanu, Dumitru
    Fractional calculus was born in 1695 on September 30 due to a very deep question raised in a letter of L'Hospital to Leibniz. The prophetical answer of Leibniz to that deep question encapsulated a huge inspiration for all generations of scientists and is continuing to stimulate the minds of contemporary researchers. During 325 years of existence, fractional calculus has kept the attention of top level mathematicians, and during the last period of time it has become a very useful tool for tackling the dynamics of complex systems from various branches of science and engineering. In this short manuscript, we briefly review the tremendous effect that the main ideas of fractional calculus had in science and engineering and briefly present just a point of view for some of the crucial problems of this interdisciplinary field.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 31
    Existence, Uniqueness and Stability Analysis of a Coupled Fractional-Order Differential Systems Involving Hadamard Derivatives and Associated With Multi-Point Boundary Conditions
    (Springer, 2021) Baleanu, Dumitru; Samei, Mohammad Esmael; Zada, Akbar; Subramanian, Muthaiah; Alzabut, Jehad
    In this paper, we examine the consequences of existence, uniqueness and stability of a multi-point boundary value problem defined by a system of coupled fractional differential equations involving Hadamard derivatives. To prove the existence and uniqueness, we use the techniques of fixed point theory. Stability of Hyers-Ulam type is also discussed. Furthermore, we investigate variations of the problem in the context of different boundary conditions. The current results are verified by illustrative examples.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    Comparison Principles of Fractional Differential Equations With Non-Local Derivative and Their Applications
    (Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Al-Refai, Mohammed
    In this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.
  • Article
    Citation - WoS: 234
    Citation - Scopus: 302
    On a Fractional Operator Combining Proportional and Classical Differintegrals
    (Mdpi, 2020) Fernandez, Arran; Akgul, Ali; Baleanu, Dumitru
    The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function <mml:semantics>f(t)</mml:semantics>, by a fractional integral operator applied to the derivative <mml:semantics>f ' (t)</mml:semantics>. We define a new fractional operator by substituting for this <mml:semantics>f ' (t)</mml:semantics> a more general proportional derivative. This new operator can also be written as a Riemann-Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann-Liouville integral and a Caputo derivative. We then conduct some analysis of the new definition: constructing its inverse operator and Laplace transform, solving some fractional differential equations using it, and linking it with a recently described bivariate Mittag-Leffler function.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 16
    The Invariant Subspace Method for Solving Nonlinear Fractional Partial Differential Equations With Generalized Fractional Derivatives
    (Springeropen, 2020) Kader, Abass H. Abdel; Baleanu, Dumitru; Latif, Mohamed S. Abdel; Abdel Latif, Mohamed S.; Abdel Kader, Abass H.
    In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter-Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman-Broer-Kaup-type equation, and a system of time fractional diffusion equations.