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  • Fractional Order Computing and Modeling with Portending Complex Fit Real-World Data 
    Karaca, Yeliz; Rahman, Mati ur; Baleanu, Dumitru (2023)
    Fractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic ...
  • Fractional order continuity of a time semi-linear fractional diffusion-wave system 
    Phuong, Nguyen Duc; Hoan, Luu Vu Cam; Karapınar, Erdal; Singh, Jagdev; Binh, Ho Duy; Can, Nguyen Huu (2020-12)
    In this work, we consider the time-fractional diffusion equations depend on fractional orders. In more detail, we study on the initial value problems for the time semi-linear fractional diffusion-wave system and discussion ...
  • Fractional Order Mathematical Model of Serial Killing with Different Choices of Control Strategy 
    Rahman, Mati Ur; Ahmad, Shabir; Arfan, Muhammad; Akgül, Ali; Jarad, Fahd (2022-03)
    The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag–Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem ...
  • Fractional Order Modelling of Zero Length Column Desorption Response For Adsorbents With Variable Particle Sizes 
    Tenreiro Machado, J. A.; Zaman, Sharif F.; Baleanu, Dumitru (Sciendo, 2013-06)
    This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena ...
  • Fractional order models of industrial pneumatic controllers 
    Razminia, Abolhassan; Baleanu, Dumitru (2014)
    This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure ...
  • Fractional Pais-Uhlenbeck Oscillator 
    Baleanu, Dumitru; Petras, Ivo; Asad, Jihad H.; Pilar Velasco, Maria (Springer, 2012-04)
    In this paper we study the fractional Lagrangian of Pais-Uhlenbeck oscillator. We obtained the fractional Euler-Lagrangian equation of the system and then we studied the obtained Euler-Lagrangian equation numerically. The ...
  • Fractional partial random differential equations with infinite delay 
    Heris, Amel; Salim, Abdelkrim; Benchohra, Mouffak; Karapınar, Erdal (2022-06)
    The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with infinite delay. The arguments are based on a random fixed point theorem with stochastic ...
  • Fractional physical problems including wind-influenced projectile motion with mittag-leffler kernel 
    Özarslan, Ramazan; Baş, Erdal; Baleanu, Dumitru; Acay, Bahar (2020)
    In this manuscript the fractional form of wind-influenced projectile motion equations which have a significant place in physics is extensively investigated by preserving dimensionality of the physical quantities for ...
  • Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative 
    Riaz, Muhammad Bilal; Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana (2022-03)
    This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa–Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with ...
  • Fractional Proportional Differences With Memory 
    Abdeljawad, Thabet; Jarad, Fahd; Alzabut, Jehad (Springer Heidelberg, 2017-12)
    In this paper, we formulate nabla fractional sums and differences and the discrete Laplace transform on the time scale hZ. Based on a local type h-proportional difference (without memory), we generate new types of fractional ...
  • Fractional radiative transfer equation within Chebyshev spectral approach 
    Kadem, Abdelouhab; Baleanu, Dumitru (Pergamon-Elsevier Science, 2010-03)
    In this work we report the convergence of the Chebyshev polynomials combined with the S(N) method for the steady state transport equation using the fractional derivative. The procedure is based on the expansion of the ...
  • Fractional Rényi Entropy Image Enhancement for Deep Segmentation of Kidney MRI 
    Jalab, Hamid A.; Al-Shamasneh, Ala'a R.; Shaiba, Hadil; Ibrahim, Rabha W.; Baleanu, Dumitru (2021)
    Recently, many rapid developments in digital medical imaging have made further contributions to health care systems. The segmentation of regions of interest in medical images plays a vital role in assisting doctors with ...
  • Fractional spectral differentiation matrices based on Legendre approximation 
    Ghorbani, Asghar; Baleanu, Dumitru (2020-03-26)
    A simple scheme is proposed for computing NxN spectral differentiation matrices of fractional order alpha for the case of Legendre approximation. The algorithm derived here is based upon a homogeneous three-term recurrence ...
  • Fractional Sub-Equation Method For The Fractional Generalized Reaction Duffing Model and Nonlinear Fractional Sharma-Tasso-Olver Equation 
    Jafari, Hossein; Tajadodi, Haleh; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H. (De Gruyter Poland SP Zoo, 2013-10)
    In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is ...
  • Fractional Subequation Method for Cahn-Hilliard and Klein-Gordon Equations 
    Jafari, Hossein; Tajadodi, Haleh; Kadkhoda, Nematollah; Baleanu, Dumitru (Hindawi LTD, 2013)
    The fractional subequation method is applied to solve Cahn-Hilliard and Klein-Gordon equations of fractional order. The accuracy and efficiency of the scheme are discussed for these illustrative examples.
  • Fractional sums and differences with binomial coefficients 
    Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Agarwal, Ravi P. (Hindawi Publishing Corp., 2013)
    In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional ...
  • Fractional synchronization of chaotic systems with different orders 
    Razminia, Abolhassan; Baleanu, Dumitru (Editura Acad Romane, 2012-12)
    In this paper, we consider two chaotic systems with different orders. First, we consider the case when one of them is fractional order (master system) and another one is integer order (slave system). Second, we consider ...
  • Fractional time action and perturbed gravity 
    Sadallah, Madhat; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab (World Scientific, 2011-06)
    In this paper, we used the scaling concepts of Mandelbrot of fractals in variational problems of mechanical systems in order to re-write the action integral function as an integration over the fractional time. In addition, ...
  • Fractional Transmission Line with Losses 
    Gómez-Aguilar, José Francisco; Baleanu, Dumitru (2014-11)
    In this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. ...
  • Fractional Treatment: An Accelerated Mass-Spring System 
    Defterli, Ozlem; Baleanu, Dumitru; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H. (2022)
    The aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and ...