Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Now showing 1 - 10 of 18
  • 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.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 8
    The Dynamic and Discrete Systems of Variable Fractional Order in the Sense of the Lozi Structure Map
    (Amer inst Mathematical Sciences-aims, 2022) Natiq, Hayder; Baleanu, Dumitru; Ibrahim, Rabha W.; Al-Saidi, Nadia M. G.
    The variable fractional Lozi map (VFLM) and the variable fractional flow map are two separate systems that we propose in this inquiry. We study several key dynamics of these maps. We also investigate the sufficient and necessary requirements for the stability and asymptotic stability of the variable fractional dynamic systems. As a result, we provide VFLM with the necessary criteria to produce stable and asymptotically stable zero solutions. Furthermore, we propose a combination of these maps in control rules intended to stabilize the system. In this analysis, we take the 1D-and 2D-controller laws as givens.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 4
    Optical Applications of a Generalized Fractional Integro-Differential Equation With Periodicity
    (Amer inst Mathematical Sciences-aims, 2023) Ibrahim, Rabha W.; Baleanu, Dumitru
    Impulsive is the affinity to do something without thinking. In this effort, we model a mathematical formula types integro-differential equation (I-DE) to describe this behavior. We investigate periodic boundary value issues in Banach spaces for fractional a class of I-DEs with non -quick impulses. We provide numerous sufficient conditions of the existence of mild outcomes for I-DE utilizing the measure of non-compactness, the method of resolving domestic, and the fixed point result. Lastly, we illustrate a set of examples, which is given to demonstrate the investigations key findings. Our findings are generated some recent works in this direction.
  • Article
    Citation - WoS: 21
    Citation - Scopus: 27
    Modified Atangana-Baleanu Fractional Operators Involving Generalized Mittag-Leffler Function
    (Elsevier, 2023) Samraiz, Muhammad; Mehmood, Ahsan; Baleanu, Dumitru; Rahman, Gauhar; Naheed, Saima; Huang, Wen-Hua
    In this paper, we are going to deal with fractional operators (FOs) with non-singular ker-nels which is not an easy task because of its restriction at the origin. In this work, we first show the boundedness of the extended form of the modified Atangana-Baleanu (A-B) Caputo fractional derivative operator. The generalized Laplace transform is evaluated for the introduced operator. By using the generalized Laplace transform, we solve some fractional differential equations. The corresponding form of the Atangana-Baleanu Caputo fractional integral operator is also estab-lished. This integral operator is proved bounded and obtained its Laplace transform. The existence and Hyers-Ulam stability is explored. In the last results, we studied the relation between our defined operators. The operators in the literature are obtained as special cases for these newly explored FOs.& COPY; 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
  • Article
    Citation - WoS: 12
    Citation - Scopus: 11
    Ulam-Hyers Stability for Tripled System of Weighted Fractional Operator With Time Delay
    (Springer, 2021) Jarad, Fahd; Abdeljawad, Thabet; Almalahi, Mohammed A.; Panchal, Satish K.
    This study is aimed to investigate the sufficient conditions of the existence of unique solutions and the Ulam-Hyers-Mittag-Leffler (UHML) stability for a tripled system of weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in the frame of Chebyshev and Bielecki norms with time delay. The acquired results are obtained by using Banach fixed point theorems and the Picard operator (PO) method. Finally, a pertinent example of the results obtained is demonstrated.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 15
    Measure Pseudo Almost Automorphic Solution To Second Order Fractional Impulsive Neutral Differential Equation
    (Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Grayna, Jeyakumar; Kavitha, Velusamy
    We discuss the concept of pseudo almost automorphic solution to fractional neutral differential equation with impulses using measure theory. Our principal results are obtained via semigroup theory and the fixed point theorem due to Krasnoselskii and their combination with the properties of measure theory. An example is provided to outline the thought developed on this work.
  • Article
    Hyers-ulam-mittag-leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform
    (2022) Ganesh, Anumanthappa; Deepa, Swaminathan; Baleanu, Dumitru; Santra, Shyam Sundar; Moaaz, Osama; Govindan, Vediyappan; Ali, Rifaqat
    In this paper, we discuss standard approaches to the Hyers-Ulam Mittag Leffler problem of fractional derivatives and nonlinear fractional integrals (simply called nonlinear fractional differential equation), namely two Caputo fractional derivatives using a fractional Fourier transform. We prove the basic properties of derivatives including the rules for their properties and the conditions for the equivalence of various definitions. Further, we give a brief basic Hyers-Ulam Mittag Leffler problem method for the solving of linear fractional differential equations using fractional Fourier transform and mention the limits of their usability. In particular, we formulate the theorem describing the structure of the Hyers-Ulam Mittag Leffler problem for linear two-term equations. In particular, we derive the two Caputo fractional derivative step response functions of those generalized systems. Finally, we consider some physical examples, in the particular fractional differential equation and the fractional Fourier transform. © 2022 the Author(s), licensee AIMS Press.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 10
    Fractional-Order Investigation of Diffusion Equations Via Analytical Approach
    (Frontiers Media Sa, 2021) Khan, Hassan; Mustafa, Saima; Mou, Lianming; Baleanu, Dumitru; Liu, Haobin
    This research article is mainly concerned with the analytical solution of diffusion equations within a Caputo fractional-order derivative. The motivation and novelty behind the present work are the application of a sophisticated and straight forward procedure to solve diffusion equations containing a derivative of a fractional-order. The solutions of some illustrative examples are calculated to confirm the closed contact between the actual and the approximate solutions of the targeted problems. Through analysis it is shown that the proposed solution has a higher rate of convergence and provides a closed-form solution. The small number of calculations is the main advantage of the proposed method. Due to a comfortable and straight forward implementation, the suggested method can be utilized to nonlinear fractional-order problems in various applied science branches. It can be extended to solve other physical problems of fractional-order in multiple areas of applied sciences.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Fractional Differential Equation With a Complex Potential
    (Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, Dumitru
    In this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 7
    A Novel Analytical Technique of the Fractional Bagley-Torvik Equations for Motion of a Rigid Plate in Newtonian Fluids
    (Tech Science Press, 2020) Ramadan, Mohamed A.; Baleanu, Dumitru; Moatimid, Galal M.; Taha, Mahmoud H.
    The current paper is concerned with a modified Homotopy perturbation technique. This modification allows achieving an exact solution of an initial value problem of the fractional differential equation. The approach is powerful, effective, and promising in analyzing some classes of fractional differential equations for heat conduction problems and other dynamical systems. To crystallize the new approach, some illustrated examples are introduced.