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, DumitruPublisher: search.filters.publisher.Iop Publishing Ltd

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  • Article
    Citation - WoS: 37
    Citation - Scopus: 37
    Advanced Fractional Calculus, Differential Equations and Neural Networks: Analysis, Modeling and Numerical Computations
    (Iop Publishing Ltd, 2023) Karaca, Yeliz; Vazquez, Luis; Macias-Diaz, Jorge E.; Baleanu, Dumitru
    Most physical systems in nature display inherently nonlinear and dynamical properties; hence, it would be difficult for nonlinear equations to be solved merely by analytical methods, which has given rise to the emerging of engrossing phenomena such as bifurcation and chaos. Conjointly, due to nonlinear systems' exhibiting more exotic behavior than harmonic distortion, it becomes compelling to test, classify and interpret the results in an accurate way. For this reason, avoiding preconceived ideas of the way the system is likely to respond is of pivotal importance since this facet would have effect on the type of testing run and processing techniques used in nonlinear systems. Paradigms of nonlinear science may suggest that it is 'the study of every single phenomenon' due to its interdisciplinary nature, which is another challenge encountered and needs to be addressed by generating and designing a systematic mathematical framework where the complexity of natural phenomena hints the requirement of identifying their commonalties and classifying their various manifestations in different nonlinear systems. Studying such common properties, concepts or paradigms can enable one to gain insight into nonlinear problems, their essence and consequences in a broad range of disciplines all forthwith. Fractional differential equations associated with non-local phenomena in physics have arisen as a powerful mathematical tool within a multidisciplinary research framework. Fractional differential equations, as one extension of the fractional calculus theory, can yield the evolution of various systems properly, which reinforces its position in mathematics and science while setting stage for the description of dynamic, complicated and nonlinear events. Through the reflection of the systems' actual properties, fractional calculus manifests unforeseeable and hidden variations, and thus, enables integration and differentiation, with the solutions to be approximated by numerical methods along with modeling and predicting the dynamics of multiphysics, multiscale and physical systems. Neural Networks (NNs), consisting of hidden layers with nonlinear functions that have vector inputs and outputs, are also considerably employed owing to their versatile and efficient characteristics in classification problems as well as their sophisticated neural network architectures, which make them capable of tackling complicated governing partial differential equation problems. Furthermore, partial differential equations are used to provide comprehensive and accurate models for many scientific phenomena owing to the advancements of data gathering and machine learning techniques which have raised opportunities for data-driven identification of governing equations derived from experimentally observed data. Given these considerations, while many problems are solvable and have been solved, efforts are still needed to be able to respond to the remaining open questions in the fields that have a broad range of spectrum ranging from mathematics, physics, biology, virology, epidemiology, chemistry, engineering, social sciences to applied sciences. With a view of different aspects of such questions, our special issue provides a collection of recent research focusing on the advances in the foundational theory, methodology and topical applications of fractals, fractional calculus, fractional differential equations, differential equations (PDEs, ODEs, to name some), delay differential equations (DDEs), chaos, bifurcation, stability, sensitivity, machine learning, quantum machine learning, and so forth in order to expound on advanced fractional calculus, differential equations and neural networks with detailed analyses, models, simulations, data-driven approaches as well as numerical computations.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 13
    The Caputo-Fabrizio Time-Fractional Sharma-Tasso Equation and Its Valid Approximations
    (Iop Publishing Ltd, 2022) Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Park, Choonkil; Salahshour, Soheil; Hosseini, Kamyar
    Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation in the Caputo-Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for phi(x, t; u) as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 9
    A Hybrid Computing Approach To Design the Novel Second Order Singular Perturbed Delay Differential Lane-Emden Model
    (Iop Publishing Ltd, 2022) Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Hincal, Evren; Sabir, Zulqurnain
    In this study, the mathematical form of the second order perturbed singular delay differential system is presented. The comprehensive features using the singular-point, perturbed factor and pantograph term are provided together with the shape factor of the second order perturbed singular delay differential system. The novel model is simulated numerically through the artificial neural networks (ANNs) based on the global/local optimization procedures, i.e., genetic algorithm (GA) and sequential quadratic programming (SQP). An activation function is constructed by using the differential model based on the second order perturbed singular delay differential system. The optimization of fitness function is performed through the hybrid computing strength of the ANNs-GA-SQP to solve the second order perturbed singular delay differential system. The exactness, substantiation, and authentication of the novel system is observed to solve three different variants of the novel model. The convergence, robustness, correctness, and stability of the numerical approach is performed using the comparison procedures of the available exact solutions. For the reliability, the statistical performances with necessary processes are provided using the ANNs-GA-SQP.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 66
    Fractional Variational Principles With Delay
    (Iop Publishing Ltd, 2008) Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Maaraba, Thabet
    The fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed. The corresponding Euler Lagrange equations are obtained and one example is analyzed in detail.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 14
    Transmission of High-Frequency Waves in a Tranquil Medium With General Form of the Vakhnenko Dynamical Equation
    (Iop Publishing Ltd, 2020) Ali, Asghar; Baleanu, Dumitru; Seadawy, Aly
    In this new work, two novel modified mathematical methods, called simple equation and F-expansion are devised for exact solutions of Vakhnenko equation, used to handle the transmission of high-frequency waves in a tranquil medium.The constructed results are in exponential, trigonometric and hyperbolic functions. By conveying the specific values for parameters, diverse form of 2D and 3D waves are generated with assistance of Mathematica. The developed solutions are fruitful in NPDEs.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 79
    Structure of Optical Soliton Solution for Nonliear Resonant Space-Time Schrodinger Equation in Conformable Sense With Full Nonlinearity Term
    (Iop Publishing Ltd, 2020) Al-Smadi, Mohammed; Al-Omari, Shrideh; Baleanu, Dumitru; Momani, Shaher; Alabedalhadi, Mohammed
    Nonclassical quantum mechanics along with dispersive interactions of free particles, long-range boson stars, hydrodynamics, harmonic oscillator, shallow-water waves, and quantum condensates can be modeled via the nonlinear fractional Schrodinger equation. In this paper, various types of optical soliton wave solutions are investigated for perturbed, conformable space-time fractional Schrodinger model competed with a weakly nonlocal term. The fractional derivatives are described by means of conformable space-time fractional sense. Two different types of nonlinearity are discussed based on Kerr and dual power laws for the proposed fractional complex system. The method employed for solving the nonlinear fractional resonant Schrodinger model is the hyperbolic function method utilizing some fractional complex transformations. Several types of exact analytical solutions are obtained, including bright, dark, singular dual-power-type soliton and singular Kerr-type soliton solutions. Moreover, some graphical simulations of those solutions are provided for understanding the physical phenomena.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 16
    Soliton Solutions of Nonlinear Boussinesq Models Using the Exponential Function Technique
    (Iop Publishing Ltd, 2021) Baleanu, Dumitru; Nawaz, Sidra; Rezazadeh, Hadi; Javeed, Shumaila
    This paper deals with the new analytical solutions of conformable nonlinear Boussinesq equations. Boussinesq equation is one of the important equation in the field of applied mathematics and engineering, particularly in optical fibers, plasma physics, fluid dynamics, signal processing, and shallow water etc. The focus of this paper is to obtain the new explicit solutions of conformable Boussinesq equations. Exponential function technique is employed to solve the considered models. The conformable properties are utilized to obtain new analytical solutions for this type of nonlinear Boussinesq equations. The new analytical solutions are acquired especially for the space-time boussinesq equation. The results are shown graphically. The obtained solutions can be useful for engineers and physicists to further analyze the phenomena. The implemented technique is valuable for finding new analytical solutions of nonlinear partial differential equations (PDEs).
  • Article
    Citation - WoS: 3
    Citation - Scopus: 5
    Simpson's Method for Fractional Differential Equations With a Non-Singular Kernel Applied To a Chaotic Tumor Model
    (Iop Publishing Ltd, 2021) Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; Arshad, Sadia; Saleem, Iram
    This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 19
    Quasi Binormal Schrodinger Evolution of Wave Polarization Field of Light With Repulsive Type
    (Iop Publishing Ltd, 2021) Demirkol, Ridvan Cem; Khalil, Eied M.; Korpinar, Zeliha; Baleanu, Dumitru; Inc, Mustafa; Korpinar, Talat
    In this paper, we study the evolution of the wave polarization vector in the tangent direction of the curved path. This path is assumed to be the trajectory of the propagated light beam. The polarization state of the wave is described by the unit complex transverse field component by eliminating the longitudinal field component. We obtain new relationship between the geometric phase and the parallel transportation law of the wave polarization vector of the evolving light beam in the tangent direction of the curved path. Moreover, we present a new geometric interpretation of the quasi binormal evolution of the wave polarization vector via the nonlinear Schrodinger equation of repulsive type in the tangent direction. Finally, we find a space-time nonlocal NLS reduction for equation system.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 5
    Ginzburg Landau Equation's Innovative Solution (Gleis)
    (Iop Publishing Ltd, 2021) Rezazadeh, Hadi; Baleanu, Dumitru; Desta Leta, Temesgen; Javeed, Shumaila; Alimgeer, Khurram Saleem; El Achab, Abdelfattah; Achab, Abdelfattah E.L.; Leta, Temesgen Desta
    A novel soliton solution of the famous 2D Ginzburg-Landau equation is obtained. A powerful Sine-Gordon expansion method is used for acquiring soliton solutions 2D Ginzburg-Landau equation. These solutions are obtained with the help of contemporary software (Maple) that allows computation of equations within the symbolic format. Some new solutions are depicted in the forms of figures. The Sine-Gordon method is applicable for solving various non-linear complex models such as, Quantum mechanics, plasma physics and biological science.