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, DumitruPublisher: search.filters.publisher.Springeropen

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  • Article
    Citation - WoS: 14
    Citation - Scopus: 18
    Existence Theory and Numerical Simulation of HIV-I Cure Model with New Fractional Derivative Possessing a Non-Singular Kernel
    (Springeropen, 2019) Aliyu, Aliyu Lsa; Alshomrani, Ali Saleh; Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru
    In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana-Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard-Lindelof has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.
  • Erratum
    Citation - WoS: 5
    Citation - Scopus: 1
    Retracted: Retracted: Fuzzy Fractional Ostrowski Inequality With Caputo Differentiability (Retracted Article. See 2013)
    (Springeropen, 2013) Allahviranloo, Tofigh; Avazpour, Lutfi; Ebadi, Mohammad J.; Baleanu, Dumitru; Salahshour, Soheil
    The use of fractional inequalities in mathematical models is increasingly widespread in recent years. In this manuscript, we firstly propose the right Caputo derivative of fuzzy-valued functions about fractional order v (0 < v < 1). To this end, we consider two types of differentiability (similar to the non-fractional case). Then we derive the equivalent integral forms of original fuzzy fractional differential equations. Finally, we prove the fuzzy Ostrowski inequality involving three functions under Caputo's differentiability. In this regard, we state some new results.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 75
    The Extended Fractional Caputo-Fabrizio Derivative of Order 0 ≤ Σ < 1 on Cr[0,1] and the Existence of Solutions for Two Higher-Order Series-Type Differential Equations
    (Springeropen, 2018) Mousalou, Asef; Rezapour, Shahram; Baleanu, Dumitru
    We extend the fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and investigate two higher-order series-type fractional differential equations involving the extended derivation. Also, we provide an example to illustrate one of the main results.
  • Article
    On a new class of fractional operators
    (Springeropen, 2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru
    This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 25
    Attractivity for a K-Dimensional System of Fractional Functional Differential Equations and Global Attractivity for a K-Dimensional System of Nonlinear Fractional Differential Equations
    (Springeropen, 2014) Nazemi, Sayyedeh Zahra; Rezapour, Shahram; Baleanu, Dumitru
    In this paper, we present some results for the attractivity of solutions for a k-dimensional system of fractional functional differential equations involving the Caputo fractional derivative by using the classical Schauder's fixed-point theorem. Also, the global attractivity of solutions for a k-dimensional system of fractional differential equations involving Riemann-Liouville fractional derivative are obtained by using Krasnoselskii's fixed-point theorem. We give two examples to illustrate our main results.
  • Article
    Citation - WoS: 24
    Citation - Scopus: 19
    Refinement Multidimensional Dynamic Inequalities With General Kernels and Measures
    (Springeropen, 2019) Rezk, Haytham M.; Abohela, Islam; Baleanu, Dumitru; Saker, Samir H.
    Using the properties of superquadratic and subquadratic functions, we establish some new refinement multidimensional dynamic inequalities of Hardy's type on time scales. Our results contain some of the recent results related to classical multidimensional Hardy's and Polya-Knopp's inequalities on time scales. To show motivation of the paper, we apply our results to obtain some particular multidimensional cases and provide refinements of some Hardy-type inequalities known in the literature.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Determination of Source Term for the Fractional Rayleigh-Stokes Equation With Random Data
    (Springeropen, 2019) Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen-H Can; Tran Thanh Binh; Binh, Tran Thanh; Luc, Nguyen Hoang; Can, Nguyen-h
    In this article, we consider the problem of finding a source term of a Rayleigh-Stokes equation. Our problem is not well-posed in the sense of Hadamard. The sought solution does not depend continuously on the given data. Using the truncation method and some new techniques on trigonometric estimators, we give the regularized solution. Moreover, the mean square error and convergence rates are established.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 16
    Reconstructing the Right-Hand Side of a Fractional Subdiffusion Equation From the Final Data
    (Springeropen, 2020) Baleanu, Dumitru; Long, Le Dinh; Can, Nguyen-Huu; Luc, Nguyen Hoang
    In this study, we study an inverse source problem for the time-fractional diffusion equation, where the final data t=Tare given. We show that our problem is ill-posed in the sense of Hadamard. Applying a truncation method, we give the regularized solution. Finally, convergence estimates under a priori and a posteriori parameter choice rules are proved.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    Fractional Spectral Differentiation Matrices Based on Legendre Approximation
    (Springeropen, 2020) Baleanu, Dumitru; Ghorbani, Asghar
    A simple scheme is proposed for computing NxN spectral differentiation matrices of fractional order alpha for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence relation and is numerically stable. The matrices are then applied to numerically differentiate.
  • 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.