Fractional derivatives and periodic functions

[1]  José António Tenreiro Machado,et al.  Integer/fractional decomposition of the impulse response of fractional linear systems , 2015, Signal Process..

[2]  Jun Jiang,et al.  On the nonexistence of non-constant exact periodic solutions in a class of the Caputo fractional-order dynamical systems , 2015 .

[3]  Manuel Duarte Ortigueira,et al.  On the particular solution of constant coefficient fractional differential equations , 2014, Appl. Math. Comput..

[4]  J. Nieto,et al.  On Fractional Derivatives and Primitives of Periodic Functions , 2014, 1405.6010.

[5]  Richard L. Magin,et al.  A real regularised fractional derivative , 2012, Signal Image Video Process..

[6]  S. Sivasundaram,et al.  Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions☆ , 2011, 1108.2825.

[7]  H. Salarieh,et al.  Technical communique: On the existence of periodic solutions in time-invariant fractional order systems , 2011 .

[8]  Manuel Duarte Ortigueira,et al.  Fractional Calculus for Scientists and Engineers , 2011, Lecture Notes in Electrical Engineering.

[9]  M. Tavazoei.  Technical communique: A note on fractional-order derivatives of periodic functions , 2010 .

[10]  Mohammad Saleh Tavazoei,et al.  A proof for non existence of periodic solutions in time invariant fractional order systems , 2009, Autom..

[11]  Manuel Duarte Ortigueira,et al.  On the fractional central differences and derivatives , 2008 .

[12]  Manuel Duarte Ortigueira,et al.  Riesz potential operators and inverses via fractional centred derivatives , 2006, Int. J. Math. Math. Sci..

[13]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[14]  Michael J. Roberts,et al.  Signals and Systems: Analysis Using Transform Methods and MATLAB , 2003 .

[15]  Manuel Duarte Ortigueira,et al.  The comb signal and its Fourier transform , 2001, Signal Process..

[16]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[17]  R.N. Bracewell,et al.  Signal analysis , 1978, Proceedings of the IEEE.

[18]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[19]  R. Estrada,et al.  Introduction to the Theory of Distributions , 1994 .

[20]  Simon Haykin,et al.  Communication Systems , 2011 .

[21]  L. Schwartz.  Théorie des distributions , 1966 .

[22]  M. Lighthill.  An Introduction to Fourier Analysis and Generalised Functions , 1958 .

[23]  H. Kober.  ON FRACTIONAL INTEGRALS AND DERIVATIVES , 1940 .