Baleanu, Dumitru

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Profile URL
https://hdl.handle.net/20.500.12416/9045
Name Variants
Baleanu, Dumitru
Baleanu, D.
Balaenu, Dumitru
Bǎleanu, D.
Balea, Itru
Bale-Anti, Dumitru
Daleanu, Bunnitru
Baleanu, Umitru
Baleanu, Dumitru I.
Baleanu, DB
Baleanu, Dumitrru
Baleanu, Dumitur
Baleanu, D
Balean, Dumitru
Baleanu, Dumitru, I
Job Title
Dr. Öğr. Üyesi
Email Address
dumitru@cankaya.edu.tr
Main Affiliation
02.02. Matematik
Matematik
02. Fen-Edebiyat Fakültesi
01. Çankaya Üniversitesi
Status
Former Staff
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Scholarly Output

2367

Articles

2161

Views / Downloads

59873/35294

Supervised MSc Theses

0

Supervised PhD Theses

0

WoS Citation Count

71654

Scopus Citation Count

79679

Patents

0

Projects

0

WoS Citations per Publication

30.27

Scopus Citations per Publication

33.66

Open Access Source

1220

Supervised Theses

0

JournalCount
Advances in Difference Equations198
AIMS Mathematics80
Abstract and Applied Analysis64
Symmetry60
Mathematical Methods in the Applied Sciences57
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Now showing 1 - 10 of 2360
  • Thumbnail Image
    Article
    Citation - Scopus: 18
    Role of Magnetic Field on the Dynamical Analysis of Second Grade Fluid: An Optimal Solution Subject to Non-Integer Differentiable Operators
    (Shahid Chamran University of Ahvaz, 2021) Baleanu, Dumitru; Riaz, Muhammad Bilal; Saeed, Syed Tauseef
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    Article
    Citation - WoS: 10
    Citation - Scopus: 8
    Derivation of Operational Matrix of Rabotnov Fractional-Exponential Kernel and Its Application To Fractional Lienard Equation
    (Elsevier, 2020) Gomez-Aguilar, J. F.; Lavin-Delgado, J. E.; Baleanu, D.; Kumar, Sachin
    Our motive in this contribution is to find out the operational matrix of fractional derivative having non singular kernel namely Rabotnov fractional-exponential (RFE) kernel which is recently introduced and seeking numerical solution of non-linear Lienard equation which have Rabotnov fractional-exponential kernel fractional derivative. First we derive an approximation formula of the fractional order derivative of polynomial function z(k) in term of RFE kernel. Using this formula and some properties of shifted Legendre polynomials, we find out the operational matrix of fractional order differentiation. In the author of knowledge this operational matrix of RFE kernel fractional derivative is derived first time. We solve a new class of fractional partial differential equation (FPDEs) by implementation of this newly derived operational matrix. We show that our newly derived operational matrix is valid by taking an fractional derivative of a polynomial. Also, we study a new model of Lienard equation with RFE kernel fractional derivative and we can easily predict the feasibility of our numerical method to this new model. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
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    Article
    Citation - WoS: 12
    Citation - Scopus: 12
    Analysis of Fractional Non-Linear Diffusion Behaviors Based on Adomian Polynomials
    (Vinca inst Nuclear Sci, 2017) Baleanu, Dumitru; Luo, Wei-Hua; Wu, Guo-Cheng
    A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.
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    Article
    Citation - WoS: 17
    Citation - Scopus: 18
    New Study of Weakly Singular Kernel Fractional Fourth-Order Partial Integro-Differential Equations Based on the Optimum Q-Homotopic Analysis Method
    (Elsevier, 2017) Darzi, Rahmat; Agheli, Bahram; Baleanu, Dumitru
    In this study, the optimum q-homotopic analysis method is employed to solve fourth order partial integro-differential equations with high-order non-integer derivatives. Several specific and clear examples are also given to illustrate the simplicity and capacity of the proposed approach. All of the computations were performed using Mathematica. (C) 2017 Elsevier B.V. All rights reserved.
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    Article
    Citation - WoS: 215
    Citation - Scopus: 250
    Discrete Fractional Differences With Nonsingular Discrete Mittag-Leffler Kernels
    (Springeropen, 2016) Abdeljawad, Thabet; Baleanu, Dumitru
    In this manuscript we propose the discrete versions for the recently introduced fractional derivatives with nonsingular Mittag-Leffler function. The properties of such fractional differences are studied and the discrete integration by parts formulas are proved. Then a discrete variational problem is considered with an illustrative example. Finally, some more tools for these derivatives and their discrete versions have been obtained.
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    Article
    Citation - WoS: 52
    Citation - Scopus: 57
    Damped Wave Equation and Dissipative Wave Equation in Fractal Strings Within the Local Fractional Variational Iteration Method
    (Springer international Publishing Ag, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein; Su, Wei-Hua
    In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions. MSC: 74H10, 35L05, 28A80.
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    Article
    Citation - WoS: 19
    Citation - Scopus: 23
    On the Solvability of Mixed-Type Fractional-Order Non-Linear Functional Integral Equations in the Banach Space C(I)
    (Mdpi, 2022) Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, Dumitru; Pathak, Vijai Kumar
    This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (kappa,phi)-Riemann-Liouville along with Erdelyi-Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo's fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations.
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    Article
    Citation - WoS: 9
    Citation - Scopus: 9
    The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations With Infinite Delay
    (Hindawi Ltd, 2013) Baleanu, Dumitru; Agarwal, Ravi P.; Babakhani, Azizollah
    We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem in Omega = {y : (-infinity,b] -> R : y vertical bar(<-infinity, 0]) epsilon B} such that y vertical bar ([0,b]) is continuous and B is a phase space.
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    Conference Object
    Citation - WoS: 10
    Citation - Scopus: 10
    About Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives
    (American Society of Mechanical Engineers, 2005) Baleanu, D.; Muslih, S.I.
    Recently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal's approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schrödinger equation is presented. Copyright © 2005 by ASME.
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    Article
    Citation - WoS: 28
    Citation - Scopus: 35
    Specific Wave Structures of a Fifth-Order Nonlinear Water Wave Equation
    (Elsevier, 2022) Mirzazadeh, M.; Salahshour, S.; Baleanu, D.; Zafar, A.; Hosseini, K.
    Investigated in the present paper is a fifth-order nonlinear evolution (FONLE) equation, known as a non-linear water wave (NLWW) equation, with applications in the applied sciences. More precisely, a travel-ing wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain. The Kudryashov methods (KMs) are then adopted as leading techniques to construct specific wave structures of the gov-erning model which are classified as W-shaped and other solitons. In the end, the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )