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Caputo derivatives of fractional variable order: numerical approximations
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Orientador(es)
Resumo(s)
We present a new numerical tool to solve partial differential equations
involving Caputo derivatives of fractional variable order. Three Caputo-type
fractional operators are considered, and for each one of them an approximation
formula is obtained in terms of standard (integer-order) derivatives only.
Estimations for the error of the approximations are also provided. We then
compare the numerical approximation of some test function with its exact
fractional derivative. We end with an exemplification of how the presented
methods can be used to solve partial fractional differential equations of
variable order.
Descrição
Palavras-chave
Fractional calculus Fractional variable order Fractional differential equations Approximation methods
Contexto Educativo
Citação
Editora
Elsevier