Scopus İndeksli Yayınlar Koleksiyonu

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

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Now showing 1 - 10 of 77
  • Article
    Citation - WoS: 180
    Citation - Scopus: 192
    On Fractional Calculus with General Analytic Kernels
    (Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, Dumitru
    Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 7
    About Fractional Calculus of Singular Lagrangians
    (Fuji Technology Press Ltd, 2005) Baleanu, Dumitru
    In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. We observed that if a Lagrangian is singular in the classical sense, it remains singular after being fractionally generalized. The fractional Lagrangian is non-local but its gauge symmetry was preserved despite complexity of equations in fractional cases. We generalized four examples of singular Lagrangians admitting gauge symmetry in fractional case and found solutions to corresponding Euler-Lagrange equations.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 3
    On Generalized Asymmetric Harmonic Oscillator With Quadratic Nonlinearity Within Fractional Variational Principles
    (Sage Publications Ltd, 2024) Baleanu, Dumitru; Jajarmi, Amin; Defterli, Ozlem; Mohammad, Noorhan F. AlShaikh; Asad, Jihad; AlShaikh Mohammad, Noorhan F
    This work studies the nonlinear fractional dynamics of asymmetric harmonic oscillators. The classical description of the physical system is generalized using the principles of fractional variational analysis. As a system of two-coupled fractional differential equations with a quadratic nonlinear component, the fractional Euler-Lagrange equations of the motion of the corresponding system are obtained. The Adams-Bashforth predictor-corrector numerical approach is used to approximate the system's outcomes, which are then simulated comparatively with respect to various model parameter values, including mass, linear and quadratic nonlinear stiffness, and the order of the fractional derivative. The simulations provided the possibility of investigating various dynamical behaviours within the same physical model that is generalized by the use of fractional operators.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 5
    Analytic Studies of a Class of Langevin Differential Equations Dominated by a Class of Julia Fractal Functions
    (Univ Kragujevac, Fac Science, 2024) Ibrahim, Rabha W.; Baleanu, Dumitru
    . In this investigation, we study a class of analytic functions of type Carath & eacute;o dory style in the open unit disk connected with some fractal domains. This class of analytic functions is formulated based on a kind of Langevin differential equations (LDEs). We aim to study the analytic solvability of LDEs in the advantage of geometric function theory consuming the geometric properties of the Julia fractal (JF) and other fractal connected with the logarithmic function. The analytic solutions of the LDEs are obtainable by employing the subordination theory.
  • Article
    Citation - Scopus: 14
    The Effect of Deformation of Special Relativity by Conformable Derivative
    (Sociedad Mexicana de Fisica, 2022) Al-Masaeed, M.; Rabei, E.M.; Baleanu, D.; Al-Jamel, A.
    In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium. © 2022, Revista Mexicana de Fisica. All Rights Reserved.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 11
    On Nabla Conformable Fractional Hardy-Type Inequalities on Arbitrary Time Scales
    (Springer, 2021) Baleanu, Dumitru; El-Deeb, Ahmed A.; Makharesh, Samer D.; Nwaeze, Eze R.; Iyiola, Olaniyi S.
    The main aim of the present article is to introduce some new backward difference -conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini's theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.
  • Article
    Citation - WoS: 105
    Citation - Scopus: 118
    On an Extension of the Operator With Mittag-Leffler Kernel
    (World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Al-Refai, Mohammed
    Dealing with nonsingular kernels is not an easy task due to their restrictions at origin. In this short paper, we suggest an extension of the fractional operator involving the Mittag-Leffler kernel which admits integrable singular kernel at the origin. New solutions of the related differential equations were reported together with some perspectives from the modelling viewpoint.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 25
    New Approach on Controllability of Hilfer Fractional Derivatives With Nondense Domain
    (Amer inst Mathematical Sciences-aims, 2022) Jothimani, Kasthurisamy; Ravichandran, Chokkalingam; Baleanu, Dumitru; Kumar, Devendra; Nisar, Kottakkaran Sooppy
    This work picturizes the results on the controllability of the nondense Hilfer neutral fractional derivative (HNFD). The uniqueness and controllability of HNFD are discussed with Winch theorem and Banach contraction technique. In addition, a numerical approximation is given to deal with different criteria of our results.
  • Article
    Citation - Scopus: 1
    Generalized Quantum Integro-Differential Fractional Operator With Application of 2d-Shallow Water Equation in a Complex Domain
    (Mdpi, 2021) Baleanu, Dumitru; Ibrahim, Rabha W.
    In this paper, we aim to generalize a fractional integro-differential operator in the open unit disk utilizing Jackson calculus (quantum calculus or q-calculus). Next, by consuming the generalized operator to define a formula of normalized analytic functions, we present a set of integral inequalities using the concepts of subordination and superordination. In addition, as an application, we determine the maximum and minimum solutions of the extended fractional 2D-shallow water equation in a complex domain.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Global Stability of Local Fractional Henon-Lozi Map Using Fixed Point Theory
    (Amer inst Mathematical Sciences-aims, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.
    We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.