NUMERICAL COMPUTATIONS OF THE FRACTIONAL DERIVATIVE IN IVPS, EXAMPLES IN MATLAB AND MATHEMATICA

Abdeljawad T.: On Riemann and Caputo fractional differences. Computers and Mathematics with Applications 62/2011, 1602–1611.
  Google Scholar

Arikoglu A., Ozkol I.: Solution of fractional integro-differential equations by using fractional differential transform method. Chaos, Solitons & Fractals 40(2)/2007, 521–529.
  Google Scholar

Brociek R., Słota D., Wituła R.: Reconstruction of the Thermal Conductivity Coefficient in the Time Fractional Diffusion Equation. Advances in Modelling and Control of Non-integer-Order Systems 2016, 239–247.
  Google Scholar

Caputo M.: Linear models of dissipation whose Q is almost frequency independent – II. Geophysical Journal International 13(5)/1967, 529–539.
  Google Scholar

Cui M.: Compact finite difference method for the fractional diffusion equation. Journal of Computational Physics 228/2009, 7792–7804.
  Google Scholar

Ducharne B., Sebald G., Guyomar D., Litak G.: Dynamics of magnetic field penetration into soft ferromagnets. Journal of Applied Physics 117/2015, 243907.
  Google Scholar

Huang L., Xian-Fang L., Zhao Y., Duan X.Y.: Approximate solution of fractional integro-differential equations by Taylor expansion method. Computers and Mathematics with Applications 62/2011, 1127–1134.
  Google Scholar

Jakubowska A., Walczak J.: Analysis of the Transient State in a Series Circuit of the Class RLC. Circuits, Systems and Signal Processing 35/2016, 1831–1853.
  Google Scholar

Katugampola U.N.: A new approach to generalized fractional derivatives. Bull. Math. Anal. Appl. 6(4)/2014, 1–15.
  Google Scholar

Kawala-Janik A., Podpora M., Gardecki A., Czuczwara W., Baranowski J., Bauer W.: Game controller based on biomedical signals. Methods and Models in Automation and Robotics (MMAR) 2015, 20th International Conference, 934–939.
  Google Scholar

Klamka, J., Czornik, A., Niezabitowski, M., Babiarz, A.: Controllability and minimum energy control of linear fractional discrete-time infinite-dimensional systems. Control & Automation (ICCA) 2014, 11th IEEE Conference, 1210–1214.
  Google Scholar

Lubich C.: Fractional linear multistep methods for Abel-Volterra integral equations of the second kind. Math. Comput. 45/1985, 463–469.
  Google Scholar

Momani S., Noor M.A: Numerical methods for fourth order fractional integro-differential equations. Appl. Math. Comput. 182/2006, 754–760.
  Google Scholar

Munkhammar J.D.: Riemann-Liouville fractional derivatives and the Taylor-Riemann series. UUDM Project Report 7/2004, 1–18.
  Google Scholar

New MATLAB External Interfacing Features in 2009a. MathWorks.http://www.mathworks.com/videos/new-external-interfacing-features-in-r2009a-101547.html (available 15.06.2016).
  Google Scholar

Ostalczyk P. W., Duch P., Brzeziński D. W., Sankowski D.: Order Functions Selection in the Variable-, Fractional-Order PID Controller. Advances in Modelling and Control of Non-integer-Order Systems 2014, 159–170.
  Google Scholar

Rawashdeh E.A.: Numerical solution of fractional integro-differential equations by collocation method. Applied Mathematics and Computation 176/2006, 1–6.
  Google Scholar

Saeedi H., Mohseni Moghadam M.: Numerical solution of nonlinear Volterra integro-differential equations of arbitrary order by CAS wavelets. Commun. Nonlinear Sci. Numer. Simulat. 16/2011, 1216–1226.
  Google Scholar

Schäfer I., Krüger K.: Modelling of lossy coils using fractional derivatives. Phys. D: Appl. Phys. 41/2008, 1–8.
  Google Scholar

Skruch P., Mitkowski W.: Fractional-order models of the ultracapacitors. Advances in the Theory and Applications of Non-Integer Order Systems. Springer International Publishing 2013, 281–293.
  Google Scholar

Sowa M.: A subinterval-based method for circuits with fractional order elements. Bull. Pol. Ac.: Tech. 62(3)/2014, 449–454.
  Google Scholar

Włodarczyk M., Zawadzki A.: RLC circuits in aspect of positive fractional derivatives. Scientific Works of the Silesian University of Technology: Electrical Engineering 1/2011, 75–88.
  Google Scholar