Linear Hilfer nabla fractional difference equations (Q2113759)
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scientific article; zbMATH DE number 7488810
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Linear Hilfer nabla fractional difference equations |
scientific article; zbMATH DE number 7488810 |
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Linear Hilfer nabla fractional difference equations (English)
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14 March 2022
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Summary: In this paper, we deal with the nabla analogue of Hilfer fractional derivative and obtain some of its salient properties such as composition and power rules. Further, we consider an initial value problem for a class of nonlinear Hilfer nabla fractional difference equations and obtain its equivalent Volterra summation equation, using these properties. Also, we derive expressions for general solutions of various classes of linear Hilfer nabla fractional difference equations by applying the discrete Laplace transform.
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Hilfer fractional derivative
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Riemann-Liouville fractional derivative
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Caputo fractional derivative
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nabla fractional difference
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composition rule
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power rule
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Mittag-Leffler function
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convolution
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initial value problem
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discrete Laplace transform
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