Matematik Bölümü Yayın Koleksiyonu

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

Browse

Filters

2010 - 2019132020 - 202414

Settings

Department: search.filters.department.Çankaya UniversitySubject: search.filters.subject.Fractional Differential Equation

Search Results

Now showing 1 - 10 of 27
  • Article
    Citation - WoS: 34
    Citation - Scopus: 36
    Exact Solutions of Boussinesq and Kdv-Mkdv Equations by Fractional Sub-Equation Method
    (Editura Acad Romane, 2013) Jafari, Hossein; Baleanu, Dumitru; Tajadodi, Haleh; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; Matematik
    A fractional sub-equation method is introduced to solve fractional differential equations. By the aid of the solutions of the fractional Riccati equation, we construct solutions of the Boussinesq and KdV-mKdV equations of fractional order. The obtained results show that this method is very efficient and easy to apply for solving fractional partial differential equations.
  • 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: 31
    Citation - Scopus: 40
    New Solutions of the Fractional Differential Equations With Modified Mittag-Leffler Kernel
    (Asme, 2023) Baleanu, Dumitru; Odibat, Zaid
    This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 33
    A New Fractional Derivative Operator With Generalized Cardinal Sine Kernel: Numerical Simulation
    (Elsevier, 2023) Baleanu, Dumitru; Odibat, Zaid
    In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann-Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 11
    Research on a Collocation Approach and Three Metaheuristic Techniques Based on Mvo, Mfo, and Woa for Optimal Control of Fractional Differential Equation
    (Sage Publications Ltd, 2023) Khanduzi, Raheleh; Beik, Samaneh P. A.; Baleanu, Dumitru; Ebrahimzadeh, Asiyeh; A Beik, Samaneh P
    Exploiting a comprehensive mathematical model for a class of systems governed by fractional optimal control problems is the significant focal point of the current paper. The efficiency index is a function of both control and state variables and the dynamic control system relies on Caputo fractional derivatives. The attributes of Bernoulli polynomials and their operational matrices of fractional Riemann-Liouville integrations are applied to convert the optimization problem to the nonlinear programing problem. Executing multi-verse optimizer, moth-flame optimization, and whale optimization algorithm terminate to the most excellent solution of fractional optimal control problems. A study on the advantage and performance between these approaches is analyzed by some examples. Comprehensive analysis ascertains that moth-flame optimization significantly solves the example. Furthermore, the privilege and advantage of preference with its accuracy are numerically indicated. Finally, results demonstrate that the objective function value gained by moth-flame optimization in comparison with other algorithms effectively decreased.
  • Article
    Citation - WoS: 201
    Citation - Scopus: 178
    On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation
    (Wiley, 2024) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan Sevinik; Sevinik Adigüzel, Rezan
    The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2 < alpha <= 3 is studied. The BVP is transformed into an integral equation and discussed by means of a fixed point problem for an integral operator. Conditions for the existence and uniqueness of a fixed point for the integral operator are derived via b-comparison functions on complete b-metric spaces. In addition, estimates for the convergence of the Picard iteration sequence are given. An estimate for the Green's function related with the problem is provided and employed in the proof of the existence and uniqueness theorem for the solution of the given problem. Illustrative examples are presented to support the theoretical results.
  • Article
    Citation - WoS: 61
    Citation - Scopus: 83
    Impulsive Caputo-Fabrizio Fractional Differential Equations in B-Metric Spaces
    (de Gruyter Poland Sp Z O O, 2021) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Lazreg, Jamal Eddine; Karaplnar, Erdal
    We deal with some impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces. We make use of alpha-phi-Geraghty-type contraction. An illustrative example is the subject of the last section.
  • 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.