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.26A33

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    Recovering the Space Source Term for the Fractional-Diffusion Equation With Caputo-Fabrizio Derivative
    (Springer, 2021) Nguyen Hoang Luc; Baleanu, Dumitru; Le Dinh Long; Le Nhat Huynh; Long, Le Dinh; Huynh, Le Nhat; Luc, Nguyen Hoang
    This article is devoted to the study of the source function for the Caputo-Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 15
    On the Weighted Fractional Integral Inequalities for Chebyshev Functionals
    (Springer, 2021) Nisar, Kottakkaran Sooppy; Khan, Sami Ullah; Baleanu, Dumitru; Vijayakumar, V.; Rahman, Gauhar
    The goal of this present paper is to study some new inequalities for a class of differentiable functions connected with Chebyshev's functionals by utilizing a fractional generalized weighted fractional integral involving another function G in the kernel. Also, we present weighted fractional integral inequalities for the weighted and extended Chebyshev's functionals. One can easily investigate some new inequalities involving all other type weighted fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta) as discussed in the literature. Furthermore, the obtained weighted fractional integral inequalities will cover the inequalities for all other type fractional integrals such as Katugampola fractional integrals, generalized Riemann-Liouville fractional integrals, conformable fractional integrals and Hadamard fractional integrals associated with Chebyshev's functionals with certain choices of omega(theta) and G(theta).
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    On a Kirchhoff Diffusion Equation With Integral Condition
    (Springer, 2020) Baleanu, Dumitru; Nguyen Hoang Luc; Nguyen Huu Can; Danh Hua Quoc Nam; Nam, Danh Hua Quoc; Luc, Nguyen Hoang; Can, Nguyen Huu
    This paper is devoted to Kirchhoff-type parabolic problem with nonlocal integral condition. Our problem has many applications in modeling physical and biological phenomena. The first part of our paper concerns the local existence of the mild solution in Hilbert scales. Our results can be studied into two cases: homogeneous case and inhomogeneous case. In order to overcome difficulties, we applied Banach fixed point theorem and some new techniques on Sobolev spaces. The second part of the paper is to derive the ill-posedness of the mild solution in the sense of Hadamard.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 26
    Boundary Value Problem for Nonlinear Fractional Differential Equations of Variable Order Via Kuratowski Mnc Technique
    (Springer, 2021) Baleanu, Dumitru; Souid, Mohammed Said; Hakem, Ali; Inc, Mustafa; Benkerrouche, Amar; Said Souid, Mohammed
    In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo's fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 23
    A Spectral Collocation Method for Fractional Chemical Clock Reactions
    (Springer Heidelberg, 2020) Saad, Khaled M.; Baleanu, Dumitru; Kumar, Sunil; Khader, Mohamed M.
    We implement an efficient computational scheme to study the effect of precursor consumption on chemical clock reactions. The proposed model is formulated as a system of FDEs with power kernel. This paper considers the fractional derivatives of Liouville-Caputo (LC). We use the spectral collocation method (SCM) with the help of the third-kind Chebyshev polynomials. This scheme generates the fast convergent series solutions with conveniently determinable coefficients. We compute the residual error function (REF) to satisfy the accuracy of the introduced technique. This approach is an easy and efficient tool for implementing the study of such these models. We introduce a comparison between the obtained approximate solutions and those which occurred using a previously published method and excellent agreement is reported.
  • 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: 7
    Citation - Scopus: 9
    Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators
    (Mdpi, 2020) Darzi, Rahmat; Agheli, Bahram; Baleanu, Dumitru
    A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.
  • Article
    Citation - WoS: 40
    Citation - Scopus: 49
    On Stability Analysis and Existence of Positive Solutions for a General Non-Linear Fractional Differential Equations
    (Springer, 2020) Kumar, Anoop; Baleanu, Dumitru; Khan, Aziz; Devi, Amita; Mansour Vaezpour, S.; Bashiri, Tahereh; Vaezpour, S. Mansour; Nyamoradi, Nemat
    In this article, we deals with the existence and uniqueness of positive solutions of general non-linear fractional differential equations (FDEs) having fractional derivative of different orders involving p-Laplacian operator. Also we investigate the Hyers-Ulam (HU) stability of solutions. For the existence result, we establish the integral form of the FDE by using the Green function and then the existence of a solution is obtained by applying Guo-Krasnoselskii's fixed point theorem. For our purpose, we also check the properties of the Green function. The uniqueness of the result is established by applying the Banach contraction mapping principle. An example is offered to ensure the validity of our results.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Higher-Dimensional Physical Models With Multimemory Indices: Analytic Solution and Convergence Analysis
    (Springer, 2020) Alquran, Marwan; Abdel-Muhsen, Ruwa; Momani, Shaher; Baleanu, Dumitru; Jaradat, Imad
    The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the gamma_-Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the gamma_-Maclaurin series. As for the application side, we solved versions of the higher-dimensional heat and wave models with spatial and temporal Caputo fractional derivatives in terms of a rapidly convergent gamma_-Maclaurin series. The method performed extremely well, and the projections of the obtained solutions into the integer space are compatible with solutions available in the literature. Finally, the graphical analysis showed a possibility that the Caputo fractional derivatives reflect some memory characteristics.