Fundamenta Informaticae - Volume 151, issue 1-4

Authors: Lenzi, M. K. | Lenzi, E. K. | Novatski, A. | Menechini Neto, R. | da Silva, L. R.

Article Type: Research Article

Abstract: We analyze the behavior of a system governed by a fractional diffusion equation with spherical symmetry and subjected to integro–differential boundary conditions which can simulate sorption, desorption and reaction processes. We consider the processes defined in terms of kinetic equations that couple the surface processes with the bulk dynamic enable us to describe scenarios where the surface modifies the bulk dynamics and this may change the behavior on surface. This problem is presented in terms of a general formulation satisfying the mass balance and a particular application characterized by a reversible process on the surface is analyzed. For this application, …we obtain exact solutions in terms of the Green function approach and evaluate the concentrations on the spherical surface and in the bulk for different processes. These results lead to a rich class of scenarios which can be related to an anomalous diffusion. Show more

Keywords: Fractional Time Derivative, Memory Effect, Kinetic Equation, Sorption

DOI: 10.3233/FI-2017-1496

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 341-354, 2017

Authors: Zhang, Xianmin | Zhang, Xianzhen | Cao, Hui

Article Type: Research Article

Abstract: In this paper we mainly study a kind of fractional differential equations with not instantaneous impulses, and find the equivalent equations of the impulsive system. The obtained result discovers that there exist general solution for the impulsive system. Next, an example is given to illustrate the obtained result.

Keywords: fractional differential equations, impulsive fractional differential equations, not instantaneous impulse, impulse, general solution

DOI: 10.3233/FI-2017-1497

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 355-369, 2017

Authors: Hristov, Jordan

Article Type: Research Article

Abstract: This paper focuses on an approximate analytical solution of an initial-boundary value problem of spatial-fractional partial differential diffusion equation with RiemannLiouville fractional derivative in space. The spatial correlation of the superdiffusion coefficient as a power-law has been discussed in cases of fast and slow spatial superdiffusion. Approximate closed form solutions in terms of non-linear similarity variable are based on the integral-balance method and series expansion of the assumed parabolic profile with undefined exponent. The law of the spatial and temporal propagation of the solution was the primary issue and discussed in two cases: fast and slow superdiffussion.

Keywords: approximate analytical solution, integral-balance method, spatial-fractional diffusion equation

DOI: 10.3233/FI-2017-1498

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 371-388, 2017

Authors: David, Sergio A. | Machado, J. A. Tenreiro | Trevisan, Lucas R. | Inácio Jr., Cláudio M.C. | Lopes, António M.

Article Type: Research Article

Abstract: This paper examines the time series of four important agricultural commodities, namely the soybean, corn, coffee and sugar prices. Time series can exhibit long-range dependence and persistence in their observation. The long memory feature of data is a documented fact and there has been an increasing interest in studying such concepts in the perspective of economics and finance. In this work, we start by analyzing the time series of the four commodities by means of the Fractional Fourier Transform (FrFT) to unveil time-frequency patterns in the data. In a second phase, we apply Auto Regressive Integrated Moving Average (ARIMA) and …Auto Regressive Fractionally Integrated Moving Average (ARFIMA) models for obtaining the spot price composition and predict future price. The ARFIMA process is a known class of long memory model, representing a generalization of the ARIMA algorithm. We compare the performances of the ARIMA and the ARFIMA models and we show that the ARFIMA has a superior performance for future price forecasting. Show more

Keywords: Fractional statistic systems, business and management, Fractional Fourier Transform, computer modeling and simulation

DOI: 10.3233/FI-2017-1499

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 389-408, 2017

Authors: Yang, Xiao-Jun | Srivastava, H. M. | Torres, Delfim F. M. | Zhang, Yudong

Article Type: Research Article

Abstract: We investigate local fractional nonlinear Riccati differential equations (LFNRDE) by transforming them into local fractional linear ordinary differential equations. The case of LFNRDE with constant coefficients is considered and non-differentiable solutions for special cases obtained.

Keywords: nonlinear Riccati equations, non-differentiable functions, local fractional derivatives

DOI: 10.3233/FI-2017-1500

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 409-417, 2017

Authors: Zhao, Xiao-Hu | Zhang, Yudong | Zhao, Duan | Yang, Xiaojun

Article Type: Research Article

Abstract: A non-differentiable resistor-capacitor circuit comprised of the capacitor and resistor in the fractal-time domain is first proposed in this article. The solution behavior of the corresponding local fractional ordinary differential equation is presented for the Mittag-Leffler decay defined on Cantor sets. The obtained results reveal the sufficiency of the local fractional calculus in the analysis of the fractal electrical systems.

Keywords: ordinary differential equations, Mittag-Leffler decay, electric circuit, local fractional derivative

DOI: 10.3233/FI-2017-1501

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 419-429, 2017

Authors: Tarasov, Vasily E.

Article Type: Research Article

Abstract: In this paper, we propose an “informatic” interpretation of the Riemann-Liouville and Caputo derivatives of non-integer orders as reconstruction from infinite sequence of standard derivatives of integer orders. The reconstruction is considered with respect to orders of derivatives.

Keywords: Fractional derivative, Riemann-Liouville derivative, Caputo derivative, derivations of Hadamard type, sampling theorem

DOI: 10.3233/FI-2017-1502

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 431-442, 2017

Authors: Hassani, Hossein | Dahaghin, Mohammad Shafie | Heydari, Mohammad Hossein | Eshkaftaki, Ali Bayati

Article Type: Research Article

Abstract: In this paper, we present a new optimization method based on a new class of functions, namely generalized polynomials (GPs) for solving linear and nonlinear fractional differential equations (FDEs). In the proposed method, the solution of the problem under study is expanded in terms of the GPs with fixed coefficients , free coefficients and control parameters . The initial conditions are employed to compute the fixed coefficients . The residual function and its ‖.‖2 are employed for converting the problem under consideration to an optimization one and then choosing the unknown free coefficients and control parameters …optimally. As a useful result, the necessary conditions of optimality are derived as a system of nonlinear algebraic equations with unknown free coefficients and control parameters . The validity and accuracy of the approach are illustrated by some numerical examples. The obtained results show that the proposed method is very efficient and accurate. Show more

Keywords: Optimization method, Generalized polynomials (GPs), Free coefficients, Fixed coefficients, Control parameters, Fractional differential equations (FDEs)

DOI: 10.3233/FI-2017-1503

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 443-457, 2017

Authors: Cattani, C. | Guariglia, E. | Wang, S.

Article Type: Research Article

Abstract: The α -order fractional derivative of the Dirichlet η function is computed in order to investigate the behavior of the fractional derivative of the Riemann zeta function ζ (α ) on the critical strip. The convergence of η (α ) is studied. In particular, its half-plane of convergence gives the possibility to better understand the ζ (α ) and its critical strip. As an application, two signal processing networks, corresponding to η (α ) and to its Fourier transform respectively, are shortly described.

Keywords: Fractional derivatives, Riemann ζ functions, Dirichlet η functions, signal processings, Fourier transform, critical strip

DOI: 10.3233/FI-2017-1504

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 459-472, 2017

Authors: Derdar, Nedjemeddine | Debbouche, Amar

Article Type: Research Article

Abstract: We investigate the unique solvability of a class of nonlinear nonlocal differential equations associated with degenerate linear operator at the fractional Caputo derivative. For the main results, we use the theory of fractional calculus and (L , p )-boundedness technique that based on the analysis of both strongly (L , p )-sectorial operators and strongly (L , p )-radial operators. The obtained results are applicable to degenerate fractional Cauchy and Showalter–Sidorov problems in Banach spaces. Finally, we give an application described by time-fractional order Oskolkov system.

Keywords: Degenerate nonlinear equation, fractional calculus, (L, p)-bounded operator, non-local condition

DOI: 10.3233/FI-2017-1505

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 473-485, 2017