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The Scientific World Journal
Volume 2014 (2014), Article ID 454865, 8 pages
http://dx.doi.org/10.1155/2014/454865
Research Article

Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators

Faculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119899, Russia

Received 23 January 2014; Accepted 23 February 2014; Published 30 April 2014

Academic Editors: D. Baleanu and H. Jafari

Copyright © 2014 K. Zhukovsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [25 citations]

The following is the list of published articles that have cited the current article.

  • K.V. Zhukovsky, “Harmonic generation by ultrarelativistic electrons in a planar undulator and the emission-line broadening,” Journal of Electromagnetic Waves and Applications, pp. 1–11, 2014. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “Harmonic radiation in a double-frequency undulator with account for broadening,” Moscow University Physics Bulletin, vol. 70, no. 4, pp. 232–239, 2015. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “A method of inverse differential operators using ortogonal polynomials and special functions for solving some types of differential equations and physical problems,” Moscow University Physics Bulletin, vol. 70, no. 2, pp. 93–100, 2015. View at Publisher · View at Google Scholar
  • K. Zhukovsky, “High harmonic generation in the undulators for free electron lasers,” Optics Communications, 2015. View at Publisher · View at Google Scholar
  • K. Zhukovsky, “High harmonic generation in undulators for FEL,” Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 2015. View at Publisher · View at Google Scholar
  • K.V. Zhukovsky, “Operational solution for some types of second order differential equations and for relevant physical problems,” Journal of Mathematical Analysis and Applications, 2016. View at Publisher · View at Google Scholar
  • K. Zhukovsky, “Violation of the maximum principle and negative solutions for pulse propagation in Guyer–Krumhansl model,” International Journal of Heat and Mass Transfer, vol. 98, pp. 523–529, 2016. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “The operational solution of fractional-order differential equations, as well as Black–Scholes and heat-conduction equations,” Moscow University Physics Bulletin, vol. 71, no. 3, pp. 237–244, 2016. View at Publisher · View at Google Scholar
  • K.V. Zhukovsky, “Exact solution of Guyer–Krumhansl type heat equation by operational method,” International Journal of Heat and Mass Transfer, vol. 96, pp. 132–144, 2016. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “Operational method of solution of linear non-integer ordinary and partial differential equations,” Springerplus, vol. 5, 2016. View at Publisher · View at Google Scholar
  • Konstantin Zhukovsky, “Operational Approach and Solutions of Hyperbolic Heat Conduction Equations,” Axioms, vol. 5, no. 4, pp. 28, 2016. View at Publisher · View at Google Scholar
  • Konstantin Zhukovsky, and Hari Srivastava, “Operational Solution of Non-Integer Ordinary and Evolution-Type Partial Differential Equations,” Axioms, vol. 5, no. 4, pp. 29, 2016. View at Publisher · View at Google Scholar
  • K. Zhukovsky, and A. Borisov, “Exponential parameterization of the neutrino mixing matrix: comparative analysis with different data sets and CP violation,” The European Physical Journal C, vol. 76, no. 11, 2016. View at Publisher · View at Google Scholar
  • Péter Ván, “Theories and heat pulse experiments of non-Fourier heat conduction,” Communications in Applied and Industrial Mathematics, vol. 7, no. 2, pp. 150–166, 2016. View at Publisher · View at Google Scholar
  • Zhukovsky, “Emission and tuning of harmonics in a planar two-frequency undulator with account for broadening,” Laser and Particle Beams, vol. 34, no. 3, pp. 447–456, 2016. View at Publisher · View at Google Scholar
  • P. Ván, A. Berezovski, T. Fülöp, Gy. Gróf, R. Kovács, Á. Lovas, and J. Verhás, “Guyer-Krumhansl–type heat conduction at room temperature,” EPL (Europhysics Letters), vol. 118, no. 5, pp. 50005, 2017. View at Publisher · View at Google Scholar
  • Konstantin Zhukovsky, “Exact Negative Solutions for Guyer–Krumhansl Type Equation and the Maximum Principle Violation,” Entropy, vol. 19, no. 9, pp. 440, 2017. View at Publisher · View at Google Scholar
  • M. Akbarzade, and A. Farshidianfar, “Analytic solution of transversal oscillation of quintic non-linear beam with energy balance method and global residue harmonic balance method,” Moscow University Physics Bulletin, vol. 72, no. 2, pp. 157–162, 2017. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “Undulators and generation of X-ray pulses in free-electron lasers with self-amplified spontaneous emission,” Moscow University Physics Bulletin, vol. 72, no. 2, pp. 128–143, 2017. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “Solving evolutionary-type differential equations and physical problems using the operator method,” Theoretical and Mathematical Physics, vol. 190, no. 1, pp. 52–68, 2017. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “The exponential parameterization of the neutrino mixing matrix as an SU(3) group element and an account for new experimental data,” Moscow University Physics Bulletin, vol. 72, no. 5, pp. 433–440, 2017. View at Publisher · View at Google Scholar
  • Zhukovsky, and Srivastava, “Analytical solutions for heat diffusion beyond Fourier law,” Applied Mathematics and Computation, vol. 293, pp. 423–437, 2017. View at Publisher · View at Google Scholar
  • Константин Владимирович Жуковский, and Konstantin Zhukovsky, “Решение дифференциальных уравнений эволюционного типа и физических задач с использованием операторного метода,” Teoreticheskaya i Matematicheskaya Fizika, vol. 190, no. 1, pp. 58–77, 2017. View at Publisher · View at Google Scholar
  • K. V. Zhukovsky, “A Harmonic Solution for the Hyperbolic Heat Conduction Equation and Its Relationship to the Guyer–Krumhansl Equation,” Moscow University Physics Bulletin, vol. 73, no. 1, pp. 45–52, 2018. View at Publisher · View at Google Scholar
  • K. Zhukovsky, and D. Oskolkov, “Exact harmonic solutions to Guyer–Krumhansl-type equation and application to heat transport in thin films,” Continuum Mechanics and Thermodynamics, 2018. View at Publisher · View at Google Scholar