What question did this study set out to answer?

To introduce generalized fractional Riemann-Liouville and Caputo-like derivatives for functions defined on fractal subsets of the real line.

January 29, 2016EntropyOpen Access

New Derivatives on the Fractal Subset of Real-Line

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To introduce generalized fractional Riemann-Liouville and Caputo-like derivatives for functions defined on fractal subsets of the real line.
Defined foundational mathematical functions, including Gamma, Mittag-Leffler, and Beta functions, over fractal sets.
Formulated a non-local Laplace transformation tailored for fractal spaces to solve linear and non-linear fractal differential equations.
Established generalized fractional calculus operators adapted for functions supported on fractal subsets.
Demonstrated that these non-local derivatives provide superior mathematical modeling capabilities for dynamic processes exhibiting memory effects.

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Implication

Theoretical study demonstrates generalized fractional derivatives on fractal sets, indicating enhanced capability for modeling processes with memory effects.

Cite This Study

Golmankhaneh et al. (2016) studied this question.

synapsesocial.com/papers/6a836b4d57427ee4f20045fa https://doi.org/10.3390/e18020001

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Implication

Theoretical study demonstrates generalized fractional derivatives on fractal sets, indicating enhanced capability for modeling processes with memory effects.

New Derivatives on the Fractal Subset of Real-Line

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Discussion

Implication

Cite This Study

New Derivatives on the Fractal Subset of Real-Line

Key Points

Discussion

Implication

Cite This Study

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