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A Simple Solution for the General Fractional Ambartsumian Equation
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Orientador(es)
Resumo(s)
Fractionalisation and solution of the Ambartsumian equation is considered. The general approach to fractional calculus suitable for applications in physics and engineering is described. It is shown that Liouville-type derivatives are the necessary ones, because they fully preserve backward compatibility with classical results. Such derivatives are used to define and solve the fractional Ambartsumian equation. First, a solution in terms of a slowly convergent fractional Taylor series is obtained. Then, a simple solution expressed in terms of an infinite linear combination of Mittag–Leffler functions is deduced. A fast algorithm, based on a bilinear transformation and using the fast Fourier transform, is described and demonstrated for its approximate numerical realisation.
Descrição
Funding Information:
The second author was supported by the Autonomous University of Mexico City (UACM) under the project Ccyt-2021-11.
Publisher Copyright:
© 2023 by the authors.
Palavras-chave
Ambartsumian equation bilinear transformation fractional derivative Grünwald–Letnikov Mittag–Leffler function General Materials Science Instrumentation General Engineering Process Chemistry and Technology Computer Science Applications Fluid Flow and Transfer Processes