Fundamenta Informaticae - Volume 151, issue 1-4

Authors: Zhang, Yudong | Yang, Xiao-Jun | Cattani, Carlo | Dong, Zhengchao | Yuan, Ti-Fei | Han, Liang-Xiu

Article Type: Other

DOI: 10.3233/FI-2017-1476

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. ix-xvi, 2017

Authors: Zhang, Yudong | Wang, Shuihua | Yang, Jian-Fei | Zhang, Zheng | Phillips, Preetha | Sun, Ping | Yan, Jie

Article Type: Research Article

Abstract: The Fractional Fourier transform (FRFT) is a relatively novel linear transforms that is a generalization of conventional Fourier transform (FT). FRFT can transform a particular signal to a unified time-frequency domain. In this survey, we try to present a comprehensive investigation of FRFT. Firstly, we provided definition of FRFT and its three discrete versions (weighted-type, sampling-type, and eigendecomposition-type). Secondly, we offered a comprehensive theoretical research and technological studies that consisted of hardware implementation, software implementation, and optimal order selection. Thirdly, we presented a survey on applications of FRFT to following fields: communication, encryption, optimal engineering, radiology, remote sensing, fractional calculus, …fractional wavelet transform, pseudo-differential operator, pattern recognition, and image processing. It is hoped that this survey would be beneficial for the researchers studying on FRFT. Show more

Keywords: fractional Fourier transform, discrete fractional Fourier transform, optimal order, time-frequency analysis, fractional wavelet transform, signal processing, fractional calculus

DOI: 10.3233/FI-2017-1477

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 1-48, 2017

Authors: Murugusundaramoorthy, G. | Janani, T. | Purohit, Sunil Dutt

Article Type: Research Article

Abstract: In this paper, we introduce and investigate two new subclasses of the function class ∑ of bi-univalent functions defined in the open unit disk, which are associated with fractional q -calculus operators, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a 2 | and |a 3 | for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.

Keywords: Analytic functions, Univalent functions, Bi-univalent functions, Bi-starlike and biconvex functions, Bi-Bazilevič functions, Fractional q-calculus operators

DOI: 10.3233/FI-2017-1478

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 49-62, 2017

Authors: Yang, Xiao-Jun | Machado, J.A. Tenreiro | Nieto, Juan J.

Article Type: Research Article

Abstract: A new family of the local fractional PDEs is investigated in this article. The linear, quasilinear, semilinear and nonlinear local fractional PDEs are presented. Furthermore, three types of the local fractional PDEs are discussed, namely, parabolic, hyperbolic and elliptic. Several examples illustrate the corresponding models in nonlinear mathematical physics.

Keywords: local fractional PDE, parabolic PDE, hyperbolic PDE, elliptic PDE, local fractional derivative

DOI: 10.3233/FI-2017-1479

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 63-75, 2017

Authors: Gupta, A.K. | Saha Ray, S.

Article Type: Research Article

Abstract: In this article, the authors present a new wavelet based method viz. Chebyshev wavelet method to compute the numerical solution of Riesz time-fractional Camassa-Holm equation. The approximate solutions of Riesz time-fractional Camassa-Holm equation thus obtained by two-dimensional Chebyshev wavelet method are compared with those obtained by analytical methods such as homotopy analysis method (HAM) and variational iteration method (VIM). The present scheme is quite simple, effective and appropriate for obtaining the numerical solution of the Riesz time-fractional Camassa-Holm equation.

Keywords: Camassa-Holm equation, Chebyshev wavelet method, Riesz fractional derivative, Left Riemann-Liouville derivative, Right Riemann-Liouville derivative

DOI: 10.3233/FI-2017-1480

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 77-89, 2017

Authors: Ahmad, Bashir | Ntouyas, Sotiris K. | Alsaedi, Ahmed | Hobiny, Aatef

Article Type: Research Article

Abstract: This paper is concerned with the existence and uniqueness of solutions for a coupled system of fractional differential equations with nonlocal and integral boundary conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. The results are explained with the aid of examples. The case of nonlocal strip conditions is also discussed.

Keywords: Fractional differential equations, coupled system, nonlocal conditions, integral boundary conditions, fixed point theorems

DOI: 10.3233/FI-2017-1481

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 91-108, 2017

Authors: Kailasavalli, S. | Suganya, S. | Mallika Arjunan, M.

Article Type: Research Article

Abstract: Based on concepts for semigroups, fractional calculus, resolvent operator and Banach contraction principle, this manuscript is principally involved with existence results for fractional neutral integro-differential systems with state-dependent delay in Banach spaces. To acquire the main results, our working concepts are that the functions deciding the equation fulfill certain Lipschitz conditions of local type which is similar to the hypotheses [1]. Finally an examples are additionally offered to exhibit the achieved hypotheses.

Keywords: Fractional order differential equations, state-dependent delay, Banach fixed point theorem, resolvent operators, semigroup theory

DOI: 10.3233/FI-2017-1482

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 109-133, 2017

Authors: Babaei, Afshin

Article Type: Research Article

Abstract: In this paper, an approximate solution of the fractional type Rosenau-Hyman equation according to an appropriate initial condition will be obtained with the help of the reduced differential transform method (RDTM). The fractional derivatives are described in the Caputo sense. Comparing the methodology with the homotopy perturbation method and the variational iteration method will be presented. The results show that solutions obtained by the RDTM are reliable and this method is effective for this type of nonlinear fractional partial differential equations.

Keywords: Fractional type Rosenau-Hyman equation, Fractional calculus, Reduced differential transform method

DOI: 10.3233/FI-2017-1483

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 135-143, 2017

Authors: Atangana, Abdon | Koca, Ilknur

Article Type: Research Article

Abstract: A comparative analysis of a model of thin viscous fluid sheet flow between Caputo and Caputo-Fabrizio derivative with fractional order was performed in this work. Sides-by-sides we presented some properties of both derivatives, and then we examined the existence of the exact solution of both nonlinear equations via the fixed-point theorem. A detailed study of the uniqueness of analysis for both models is presented. Numerical simulations are presented to access the difference between both models.

Keywords: Caputo derivative, Caputo-Fabrizio derivative, thin viscous fluid sheet flow model, existence and uniqueness of exact solution

DOI: 10.3233/FI-2017-1484

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 145-159, 2017

Authors: Jafari, Hossein | Lia, Atena | Tejadodi, Haleh | Baleanu, Dumitru

Article Type: Research Article

Abstract: Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional derivative is reported. We present numerical results of solving the fractional Riccati differential equations by using the variational iteration method and its modification. The obtained results of two methods demonstrate the efficiency and simplicity of the MVIM that gives good approximations for a larger interval.

Keywords: Caputo-Fabrizio derivative, Riccati differential equations, Fractional derivative

DOI: 10.3233/FI-2017-1485

Citation: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 161-171, 2017