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Keywords: fractional derivative
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Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2023, 18(4): 041004.
Paper No: CND-21-1345
Published Online: March 7, 2023
... author. e-mail:  devendra.maths@gmail.com 29 10 2021 01 02 2023 07 03 2023 Liénard's equation fractional derivative q -homotopy analysis method Sumudu transform The Liénard's equation introduced by Liénard [ 1 ] and is represented as follows: (1) u ″ + f...
Journal Articles
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. November 2019, 14(11): 111008.
Paper No: CND-19-1086
Published Online: September 23, 2019
..., telegraph, and Burgers' models that are equipped with three memory indices. In some sense, the nature of these solutions reveals that the fractional derivative parameters can be apparently considered as memory indices since the exact solutions of the integer version of these models can be obtained...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2012, 7(2): 021005.
Published Online: January 6, 2012
...Om P. Agrawal; M. Mehedi Hasan; X. W. Tangpong Fractional derivatives (FDs) or derivatives of arbitrary order have been used in many applications, and it is envisioned that in the future they will appear in many functional minimization problems of practical interest. Since fractional derivatives...
Journal Articles
Publisher: ASME
Article Type: Technical Briefs
J. Comput. Nonlinear Dynam. July 2011, 6(3): 034501.
Published Online: March 2, 2011
...Manuel D. Ortigueira; Juan J. Trujillo The generalized Grünwald–Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2011, 6(2): 021009.
Published Online: October 28, 2010
... is described by a fractional differential equation of order less than 1, and the fractional derivative is defined in terms of Riemann–Liouville. The performance index includes the terminal cost function in addition to the integral cost function. A general transversility condition in addition to the optimal...
Journal Articles
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2011, 6(2): 021003.
Published Online: October 20, 2010
... ( α ) ∫ 0 x ( x − t ) α − 1 f ( t ) d t ,     x > 0 where Γ ( ⋅ ) is the gamma function. Most commonly encountered fractional derivatives are the Riemann–Liouville fractional derivative (RLFD) and Caputo fractional derivative (CFD...