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1
Content available Exact solutions of fractional oscillator eigenfunction problem with fixed memory length
Klimek Malgorzata, Blaszczyk Tomasz
Journal of Applied Mathematics and Computational Mechanics
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2024
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Vol. 23, nr 1
45-58
EN
In this paper, the eigenproblem for a fractional oscillator under homogeneous Dirichlet and Neumann boundary conditions is considered. Key properties of fractional operators with fixed memory length are established, such as the connection between left and right operators, the product rule for fractional integrals, and the fractional integration by the parts rule for periodic/antiperiodic functions. Explicit solutions in the form of discrete sets of sine/cosine eigenfunctions are derived. The impact of fractional order and memory length on eigenvalues is presented on graphs. Finally, a comparison of eigenvalues of oscillator with a fixed memory length and infinite memory length is shown.
2
Content available remote Diophantine approximations and almost periodic functions
Nawrocki A.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
100--104
EN
In this paper we investigate the asymptotic behaviour of the classical continuous and unbounded almost periodic function in the Lebesgue measure. Using diophantine approximations we show that this function can be estimated by functions of polynomial type and we give the best polynomial estimation.
3
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
375-380
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
4
Content available remote About definition of a periodic function
Rygał G., Bryll G.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
Vol. 12
375-380
EN
In this paper we consider various definitions of a periodic function and establish connections between them, in particular, we prove equivalence of some of them. In papers and textbooks one can find different definitions of a periodic function. This raises the question which of them are equivalent.
5
Content available remote Some remarks on almost periodic functions
Adamczak M.
Fasciculi Mathematici
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2002
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Nr 33
5-19
EN
In this paper we present the definition and some properties of (IC)-a.p. functions, i.e. uniformly almost periodic (IC)(n)-a.p. functions with their indefinite integrals. Next, we give the definition and some properties of (IC)(n) -a.p. functions, i.e. uniformly almost periodic functions with their n derivatives and indefinite indegrals, and (IC)(n) -a.p. functions, i.e. uniformly almost periodic functions with their every derivatives, with respect to a positive sequence a = (a1), and indefinite integrals.
6
Content available remote On the indefinite integral and approximation of H-almost periodic functions
Stoiński S.
Fasciculi Mathematici
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1999
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Nr 29
133-137
EN
The paper gives a theorem on the indefinite integral of H-almost periodic function and a theorem on approximation of an H-almost periodic function by means Steklov functions.
7
Content available remote On compactness of almost periodic functions in the Lebesgue measure
Stoiński S.
Fasciculi Mathematici
|
1999
|
Nr 30
171-175
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