Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe change of variable formula for the Riemann integral
143
0
0.0
(
0
)
Authors
Alberto Torchinsky
Ask ChatGPT about the research
No Arabic abstract
This note concerns the general formulation by Preiss and Uher of Kestelmans influential result pertaining the change of variable, or substitution, formula for the Riemann integral.
rate research
Read More
We consider general formulations of the change of variable formula for the Riemann-Stieltjes integral, including the case when the substitution is not invertible.
In this paper, we prove a new integral representation for the Bessel function of the first kind $J_mu(z)$, which holds for any $mu,zinmathbb{C}$.
We generalize Warnaars elliptic extension of a Macdonald multiparameter summation formula to Riemann surfaces of arbitrary genus.
We prove Cauchys formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.
Several approaches to the formulation of a fractional theory of calculus of variable order have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an alternative view on the problem, originally proposed by G. Scarpi in the early seventies, based on a naive modification of the representation in the Laplace domain of standard kernels functions involved in (constant-order) fractional calculus. We frame Scarpis ideas within recent theory of General Fractional Derivatives and Integrals, that mostly rely on the Sonine condition, and investigate the main properties of the emerging variable-order operators. Then, taking advantage of powerful and easy-to-use numerical methods for the inversion of Laplace transforms of functions defined in the Laplace domain, we discuss some practical applications of the variable-order Scarpi integral and derivative.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
