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  • 1.
    Cattani, Carlo
    et al.
    University of Tuscia Largo dell’Universita, Italy.
    Guariglia, Emanuel
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Salerno, Italy.
    Wang, Shuihua
    Nanjing University, China.
    On the Critical Strip of the Riemann zeta Fractional derivative2017In: Fundamenta Informaticae, ISSN 0169-2968, E-ISSN 1875-8681, Vol. 151, p. 459-472Article in journal (Refereed)
    Abstract [en]

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

  • 2.
    Guariglia, Emanuel
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Salerno, Italy.
    Entropy and fractal antennas2016In: Entropy, ISSN 1099-4300, E-ISSN 1099-4300, Vol. 18, no 3, article id 84Article in journal (Refereed)
    Abstract [en]

    The entropies of Shannon, Rényi and Kolmogorov are analyzed and compared together with their main properties. The entropy of some particular antennas with a pre-fractal shape, also called fractal antennas, is studied. In particular, their entropy is linked with the fractal geometrical shape and the physical performance.

  • 3.
    Guariglia, Emanuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. University of Salerno, Italy.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A functional equation for the Riemann zeta fractional derivative2017In: Proceedings of INCPAA 2016, 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020063-1-020063-10, article id UNSP 020063Conference paper (Refereed)
    Abstract [en]

    In this paper a functional equation for the fractional derivative of the Riemann zeta function is presented. The fractional derivative of the zeta function is computed by a generalization of the Grunwald-Letnikov fractional operator, which satisfies the generalized Leibniz rule. It is applied to the asymmetric functional equation of the Rieman zeta function in order to obtain the result sought. Moreover, further properties of this fractional derivative are proposed and discussed.

  • 4.
    Guariglia, Emanuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Fractional Derivative of Riemann zeta function and Main Properties2016Conference paper (Other academic)
    Abstract [en]

    The Caputo-Ortigueira fractional derivative provides the fractional derivativeof complex functions. This derivative plays an important role in the number theory, and has been shown suitable for the analysis of the Dirichlet series, Hurwitz zeta function and Riemann zeta function. An integral representation for the fractional derivative of the Riemann zeta function was discovered. Since the Riemann zeta function is widely used in Physics, the unilateral Fourier transform of its fractional derivative is computed to investigate its applications in Quantum Theory and Signal Processing.

  • 5.
    Guariglia, Emanuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)2016In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Silvestrov, Sergei; Rančić, Milica, Springer, 2016, p. 337-353Chapter in book (Refereed)
    Abstract [en]

    In the following chapter we describe a wavelet expansion theory for positivedefinite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterisation of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator is rewritten as a convolution product according to the fractional calculus of real distributions. In particular, the fractional derivative of the Gabor-Morlet wavelet is computed together with its plots and main properties.

  • 6.
    Guariglia, Emanuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Qi, Xiaomin
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    A spectral analysis of the Weierstrass-Mandelbrot function on the Cantor set2016Conference paper (Other academic)
    Abstract [en]

    In this paper, the Weierstrass-Mandelbrot function on the Cantor set is presented with emphasis on possible applications in science and engineering. An asymptotic estimation of its one-sided Fourier transform, in accordance with the simulation results, is analytically derived. Moreover, a time-frequency analysis of the Weierstrass-Mandelbrot function is provided by the numerical computation of its continuous wavelet transform.

  • 7.
    Metri, Prashant G
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Guariglia, Emanuel
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink2017In: AIP Conference Proceedings, Volume 1798, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020096-1-020096-10, article id 020096Conference paper (Refereed)
    Abstract [en]

    An analysis for the MHD boundary layer flow and heat transfer towards stretching sheet is carried out via symmetry analysis. A steady two-dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow permeated by a uniform transverse magnetic field. The governing partial dierential equations are reduced to a system of ordinarydierential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations.The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary dierential equation corresponding to momentum equation and second order dierential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the eects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source/sink, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed.

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