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On Euler methods for Caputo fractional differential equations

Petr Tomášek (2023)

Archivum Mathematicum

Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations.

On expanding iteration semigroups of set-valued functions.

Łydzińska, G. (2004)

Mathematica Pannonica

On exponents of convergence of subsequences

Tibor Šalát (1984)

Czechoslovak Mathematical Journal

On extending $C^{k}$ functions from an open set to $ℝ$ with applications

Walter D. Burgess, Robert M. Raphael (2023)

Czechoslovak Mathematical Journal

For $k \in ℕ \cup {\infty}$ and $U$ open in $ℝ$ , let $C^{k} (U)$ be the ring of real valued functions on $U$ with the first $k$ derivatives continuous. It is shown that for $f \in C^{k} (U)$ there is $g \in C^{\infty} (ℝ)$ with $U \subseteq coz g$ and $h \in C^{k} (ℝ)$ with ${f g |}_{U} {= h |}_{U}$ . The function $f$ and its $k$ derivatives are not assumed to be bounded on $U$ . The function $g$ is constructed using splines based on the Mollifier function. Some consequences about the ring $C^{k} (ℝ)$ are deduced from this, in particular that $Q_{cl} (C^{k} (ℝ)) = Q (C^{k} (ℝ))$ .

On extreme first return path derivatives

Aliasghar Alikhani-Koopaei (2002)

Mathematica Slovaca

On fixed points of continuous real functions

Bartłomiej Ulewicz (1975)

Annales Polonici Mathematici

On Fourier coefficients of class $W^{r} H {(δ_{0})}_{L}$ .

Miloradovic, Slobodan (1980)

Publications de l'Institut Mathématique. Nouvelle Série

On fractional derivatives

Helena Musielak (1973)

Colloquium Mathematicae

On fractional differentiation and integration on spaces of homogeneous type.

A. Eduardo Gatto, Carlos Segovia, Stephen Vági (1996)

Revista Matemática Iberoamericana

In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before.We show that these operators act on Lipschitz spaces as in the classical cases. We prove that...

On Fractional Helmholtz Equations

Samuel, M., Thomas, Anitha (2010)

Fractional Calculus and Applied Analysis

MSC 2010: 26A33, 33E12, 33C60, 35R11In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.