Discrete Fractional Calculus

By Christopher S. Goodrich, Allan Peterson. 2016

701 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/1686b79ae900e1934fa2f9bd5bf75819b473683d

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In Modeling and Simulation

Citations in the corpus

Comparison theorems and asymptotic behavior of solutions of discrete fractional equations (2015, methodology): “We will use the following lemma which appears in [8].”
Positivity, monotonicity, and convexity for convolution operators (2020, methodology): “We refer the interested reader either to Goodrich and Peterson [20] or Goodrich and Lizama [19].”
Convexity for nabla and delta fractional differences (2015, methodology): “a H2n21ðt; rðtÞÞf ðtÞ7tþ ðt aþ2 H2n21ðt; rðtÞÞf ðtÞ7t; 1⁄4 H2n21ðt; aÞf ðaþ 1Þ þ H2n21ðt; aþ 1Þf ðaþ 2Þ þ ðt aþ2 H2n21ðt; rðtÞÞf ðtÞ7t: ð2:2Þ Using the power rule ([10]) 7tH2nðt; tÞ 1⁄4 2H2n21ðt; rðtÞÞ; and integrating by parts twice, we have for t [ Naþ4 ðt aþ2 H2n21ðt; rðtÞÞf ðtÞ7t 1⁄4 2f ðtÞH2nðt”
Two monotonicity results for nabla and delta fractional differences (2015, methodology): “The following result (see [9]) gives a formula for the ν-th fractional delta difference.”
A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity (2020, background): “For additional background on the discrete fractional calculus and related topics we direct the interested reader to the recent monograph by Goodrich and Peterson [33].”
Arbitrary Order Fractional Difference Operators with Discrete Exponential Kernels and Applications (2017, background): “For the classical fractional calculus which is behindmany extensions, we refer the reader to [32–35] and for the sake of comparison with the classical discrete fractional case we refer to [36] and the references therein.”