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Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
- solutions by mathematical methods of problems emerging in computer science
- solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, & algebraic and categorical methods.
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
Authors: Kalamani, P. | Mallika Arjunan, M. | Mallika, D. | Baleanu, D.
Article Type: Research Article
Abstract: Based on concepts for semigroup theory, fractional calculus, Banach contraction principle and Krasnoselskii fixed point theorem (FPT), this manuscript is principally involved with existence results of Riemann-Liouville (RL) fractional neutral integro-differential systems (FNIDS) with nonlocal conditions (NLCs) in Banach spaces. An example is offered to demonstrate the theoretical concepts.
Keywords: Fractional order integro-differential equations, Riemann-Liouville fractional derivatives, fixed point, semigroup theory
DOI: 10.3233/FI-2017-1506
Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 487-504, 2017
Authors: Wang, Shuihua | Yang, Ming | Li, Jianwu | Wu, Xueyan | Wang, Hainan | Liu, Bin | Dong, Zhengchao | Zhang, Yudong
Article Type: Research Article
Abstract: To detect the sensorineural hearing loss (SNHL) from healthy people accurately, we used magnetic resonance imaging (MRI) to obtain the imaging data, and then proposed a new computer-aided diagnosis (CAD) system, on the basis of texture analysis method. In the first, we extracted 12-element feature from each brain image via fractional Fourier entropy (FRFE). Afterwards, multilayer perceptron (MLP) was employed as the classifier, which was trained by a novel fitness-scaling adaptive genetic algorithm (FSAGA). The statistical analysis over 49 subjects showed the overall accuracy of our method yielded 95.51%. Experimental results performed better than four state-of-the-art weight optimization methods, and …this CAD system give significantly better performance than manual interpretation. Show more
Keywords: texture analysis, fractional Fourier entropy, power-rank fitness scaling, sensorineural hearing loss, genetic algorithm
DOI: 10.3233/FI-2017-1507
Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 505-521, 2017
Authors: Sharmaa, J. B. | Sharma, K.K. | Purohit, S.D. | Atangana, Abdon
Article Type: Research Article
Abstract: Watermarking is proposed as solution to authentication, copyright protection and security requirements of multimedia objects (speech, image and video). In this paper a watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed. In the proposed scheme, image to be watermarked is first transformed by finite radon transform, the radon transformed image is further transformed by FRFT, and singular values of FRFT transformed image are modified to embed the watermark. Inverse transformation is applied to obtain watermarked image. Simulations are performed under various test conditions with different FRFT transform angles for improved …robustness and visual transparence of watermarked image. Results of the proposed scheme are better in comparison to the existing schemes for most of the attacks. Proposed scheme provide additional degree of freedom in security, robustness, payload capacity and visual transparence. Proposed scheme can also be used to communicate or store the watermarked image as erasure code, to reduce communication errors over a network, due to the use of FRAT. Show more
Keywords: Image watermarking, Fractional Fourier transform, Finite Radon transforms, Singular Value Decomposition
DOI: 10.3233/FI-2017-1508
Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 523-543, 2017
Article Type: Other
Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 545-548, 2017
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