Zobrazeno 1 - 10
of 15
pro vyhledávání: '"Manuel D. Ortigueira"'
Autor:
Manuel D. Ortigueira
Publikováno v:
Symmetry, Vol 16, Iss 7, p 814 (2024)
This paper aims to demonstrate that, beyond the small world of Riemann–Liouville and Caputo derivatives, there is a vast and rich world with many derivatives suitable for specific problems and various theoretical frameworks to develop, correspondin
Externí odkaz:
https://doaj.org/article/9ee3f54963d4490986b2325df0910afb
Autor:
Duarte Valério, Manuel D. Ortigueira
Publikováno v:
Mathematics, Vol 11, Iss 21, p 4549 (2023)
General variable-order fractional scale derivatives are introduced and studied. Both the stretching and the shrinking cases are considered for definitions of the derivatives of the GL type and of the Hadamard type. Their properties are deduced and di
Externí odkaz:
https://doaj.org/article/98d2469df0af4ef59dbc6225f1111bb6
Autor:
Manuel D. Ortigueira, Gary W. Bohannan
Publikováno v:
Fractal and Fractional, Vol 7, Iss 4, p 296 (2023)
A general fractional scale derivative is introduced and studied. Its relation with the Hadamard derivatives is established and reformulated. A new derivative similar to the Grünwald–Letnikov’s is deduced. Tempered versions are also introduced. S
Externí odkaz:
https://doaj.org/article/923b965ba5794e138dabdef6f484b997
Publikováno v:
Journal of Advanced Research, Vol 25, Iss , Pp 11-17 (2020)
A study of non-commensurate fractional linear system is done in a parallel way to the commensurate case. A partial fraction decomposition is accomplished using a recursive procedure. Each partial fraction is inverted in two different ways. The decomp
Externí odkaz:
https://doaj.org/article/343295a5204e48c2ab574509abb16b68
Publikováno v:
Journal of Advanced Research, Vol 25, Iss , Pp 1-10 (2020)
In this paper we introduce new discrete-time derivative concepts based on the bilinear (Tustin) transformation. From the new formulation, we obtain derivatives that exhibit a high degree of similarity with the continuous-time Grünwald-Letnikov deriv
Externí odkaz:
https://doaj.org/article/523f53f8ed7e456fa8e041fe5167f425
Autor:
Müfit Şan, Manuel D. Ortigueira
Publikováno v:
Mathematics, Vol 10, Iss 23, p 4552 (2022)
We review the direct and inverse Laplace transforms on non-uniform time scales. We introduce full backward-compatible unilateral Laplace transforms and studied their properties. We also present the corresponding inverse integrals and some examples.
Externí odkaz:
https://doaj.org/article/239bf61d643a4862b139d05ca79919bc
Autor:
Manuel D. Ortigueira
Publikováno v:
Mathematics, Vol 10, Iss 19, p 3474 (2022)
In this paper, the lognormal distribution is studied, and a new series representation is proposed. This series uses the powers of the bilinear function. From it, a simplified form is obtained and used to compute the Laplace transform of the distribut
Externí odkaz:
https://doaj.org/article/52cff6da8078415da5caadcaaebb06a6
Autor:
Manuel D. Ortigueira
Publikováno v:
Mathematics, Vol 10, Iss 10, p 1771 (2022)
In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives
Externí odkaz:
https://doaj.org/article/0caf4987ef7744c3b72e362c990e94a5
Publikováno v:
Mathematics, Vol 10, Iss 5, p 737 (2022)
In this paper, we introduce a unified fractional derivative, defined by two parameters (order and asymmetry). From this, all the interesting derivatives can be obtained. We study the one-sided derivatives and show that most known derivatives are part
Externí odkaz:
https://doaj.org/article/461962c9d0334257bbc93497e986b2e8
Publikováno v:
Journal of King Saud University: Science, Vol 28, Iss 1, Pp 29-32 (2016)
The problem of steady state output of the discrete-time fractional differential systems is studied in this paper. Based on the fact that the exponentials are the eigenfunctions of such systems, a general algorithm for the output computation when the
Externí odkaz:
https://doaj.org/article/908623daf035458caff7980c086fa716