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, D.Subject: search.filters.subject.Fractional Differential Equations

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Now showing 1 - 8 of 8
  • 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 - Scopus: 10
    Solving System of Fractional Differential Equations Via Vieta-Lucas Operational Matrix Method
    (Springer, 2024) Aeri, S.; Bala, A.; Kumar, R.; Baleanu, D.; Chaudhary, R.
    Vieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and engineered problems. The classical fractional derivative due to Caputo is used to write the emerging operational matrices. These matrices are developed and evaluated by using the properties of VLPs. The residuated functions are mapped to zero by the tools of the Tau algorithm. Convergence and error analysis are thoroughly explored. Test examples for a fractional system of differential equations are borrowed from literature. The theoretical and simulated exercise on these examples authenticate the relevance of this scheme. Here, novel inclusion of Vieta-Lucas polynomials has been ensured in combination with the Tau approach. The operational matrix approach which provides extensive information about the fractional derivatives of different terms of Vieta-Lucas polynomial expansion, is ensured to operate to reduce the problem into an algebraic setup. The novelty is further enhanced by comparing the present scheme with the fourth-order Runge–Kutta method. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 16
    Analysis and Numerical Solution of the Generalized Proportional Fractional Cauchy Problem
    (Elsevier, 2021) Baleanu, D.; Makhlouf, Abdellatif Ben; Nagy, A. M.; Boucenna, Djalal; Ben Makhlouf, Abdellatif
    In this paper, we explore the existence and uniqueness theorem for a problem of the fractional Cauchy form, with dependence on the generalized proportional Caputo derivative. Furthermore, a new numerical technique is presented based on a decomposition formula for the generalized proportional Caputo derivative. Convergence analysis of the proposed technique is proved. Finally, numerical results are obtained to confirm the validity of the proposed method. (C) 2021 IMACS. Published by Elsevier reserved.
  • Article
    Citation - Scopus: 5
    Chaos Synchronization of the Fractional Rucklidge System Based on New Adomian Polynomials
    (L and H Scientific Publishing, LLC, 2017) Baleanu, D.; Huang, L.-L.; Wu, G.-C.
    The fractional Rucklidge system is a new kind of chaotic models which hold the feature of memory effects and can depict the long history interactions. A numerical formula is proposed by use of the fast Adomian polynomials. Chaotic behavior are discussed and the Poincare sections are given for various fractional cases. It's also applied in chaos synchronization of the fractional system. © 2017 L & H Scientific Publishing, LLC.
  • Article
    Citation - WoS: 45
    Citation - Scopus: 48
    Laplace 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: 9
    Citation - Scopus: 11
    Study on Application of Hybrid Functions To Fractional Differential Equations
    (Springer international Publishing Ag, 2018) Baleanu, D.; Torkzadeh, L.; Nouri, K.
    In this study we propose an efficient technique for approximate solution of linear and nonlinear differential equations with fractional order. The operational matrices based upon block-pulse functions and Chebyshev polynomials of the second kind are used for this purpose. Also, we focus on the upper bound of error for performance of the our estimates. The numerical results confirm the convergence of the suggested method. Correspondingly, the obtained results of our method are compared with other approaches in terms of efficiency and accuracy.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 41
    A Novel Approach To Approximate Fractional Derivative With Uncertain Conditions
    (Pergamon-elsevier Science Ltd, 2017) Salahshour, S.; Ali-Akbari, M.; Ismail, F.; Baleanu, D.; Ahmadian, A.
    This paper focuses on providing a new scheme to find the fuzzy approximate solution of fractional differential equations (FDEs) under uncertainty. The Caputo-type derivative base on the generalized Hukuhara differentiability is approximated by a linearization formula to reduce the corresponding uncertain FDE to an ODE under fuzzy concept. This new approach may positively affect on the computational cost and easily apply for the other types of uncertain fractional-order differential equation. The performed numerical simulations verify the proficiency of the presented scheme. (C) 2017 Published by Elsevier Ltd.