Three-Dimensional Analytical Solution of the Fractional Atmospheric Pollutant Dispersion Equation Considering Caputo and Conformable Derivatives

Prates, José Humberto de Souza; Silva, José Roberto Dantas da; Souza, Filipe Milani de; Moreira, Davidson Martins

doi:10.1007/s00024-022-03114-9

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Riemann-liouvill Fractional Derivative (Rfd) Of Order1

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2024

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“…In contrast, the Riemann -Liouville fractional derivative definition includes specific fractional derivatives (and/or integrals) of the unknown solution at the beginning point x = 0, which are functions of x. The beginning circumstances lack physical characteristics, and the method for measuring these quantities in tests is unclear, making it difficult to allocate them accurately in an analysis [26][27][28][29][30].…”

Section: Riemann-liouvill Fractional Derivative (Rfd) Of Ordermentioning

confidence: 99%

Decomposing Method for Space-Time Fractional Order PDEs

Shukur,

Jaber,

RASHEED

et al. 2024

AJEST

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Numerical solutions to integer-order differential equations frequently employ decomposition as one of many methods. This paper provides a generalization of integer-order differential equations into fractional order, which is more general, as well as generalizing the decomposing method into the fractional case and then applying it to solve differential equations of fractional order in both space and time. A fractional calculus's theorems and properties to generalize both differential equations and the decomposition method have been utilized. This method to solve different fractional time and space partial differential equations, demonstrating its ability and applicability to various problems have been applied. The method to various cases to highlight its strengths has been used. The graphs and tables of results obtained using Matlab programs have been presented and discussed.

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