Results 11 to 20 of about 122 (24)
, 2003 We formulate indefinite integration with respect to an irregular function as an algebraic problem and provide a criterion for the existence and uniqueness of a solution.
Gubinelli, Massimiliano
core +2 more sources
A new truncated $M$-fractional derivative type unifying some fractional derivative types with classical properties [PDF]
, 2017 We introduce a truncated $M$-fractional derivative type for $\alpha$-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called conformable ...
de Oliveira, E. Capelas +1 more
core +3 more sources
On the Riemann integrability of the norm of a path in normed spaces
, 2023 A useful result is that if a bounded complex-valued path is Riemann-integrable, then its modulus is also Riemann-integrable. The extension of this last result to bounded paths taking values in a normed space is affirmed, as being true, in [3].
Rivera, Luis +2 more
core
An extension of the Cartwright-McMullen theorem in fractional calculus for the smooth Stieltjes case
, 2023 In 1976, Donald Cartwright and John McMullen characterized axiomatically the Riemann-Liouvile fractional integral in a paper that was published in 1978. The motivation for their work was to answer affirmatively to a conjecture stated by J. S.
Labora, Daniel Cao
core
Evaluations of the improper integrals ∫ 0 ∞ [sin 2m (αx)]/(x 2n)] cos(bx) dx and ∫ 0 ∞ [sin 2m+1 (αx)]/(x 2n+1 )] cos(bx)dx [PDF]
, 2002 In this article, using L’Hospital rule, mathematical induction, the trigonometric power formulae and integration by parts, some integral formulae for improper integrals ∫ 0 ∞ [sin 2m (αx)]/(x 2n)] cos(bx) dx and ∫ 0 ∞ [sin 2m+1 (αx)]/(x 2n+1 )] cos(bx)dx
Luo, Qiu-Ming, Qi, Feng
core
Consistency of Markov chain quasi-Monte Carlo on continuous state spaces
, 2009 The random numbers driving Markov chain Monte Carlo (MCMC) simulation are usually modeled as independent U(0,1) random variables. Tribble [Markov chain Monte Carlo algorithms using completely uniformly distributed driving sequences (2007) Stanford Univ.]
Chen, S., Dick, J., Owen, A. B.
core +5 more sources
Henstock-Kurzweil integrals on time scales [PDF]
, 2008 A definition for a version of the Henstock-Kurzweil integral on time scales is given using covering arguments. The integral is shown to be expressible, in some situations, as an ordinary integral in the Newton, the Lebesgue, and Henstock-Kurzweil senses.
Brian S Thomson
core
The Fourier transform in Lebesgue spaces
, 2023 For each $f\in L^p({\mathbb R)}$ ($1\leq ...
Talvila, Erik
core
On the Almost Everywhere Continuity
, 2014 The aim of this paper is to provide characterizations of the Lebesgue-almost everywhere continuity of a function f : [a, b] $\rightarrow$ R. These characterizations permit to obtain necessary and sufficient conditions for the Riemann integrability of f
Blot, Joël
core +1 more source
Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
, 2001 A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional ...
Podlubny, Igor
core +2 more sources