Real Analysis

Follow this topic

Answer added to:
2 What sense have derived fractional to control theory?
By Jessica Mendiola · Instituto Potosino de Investigación Científica y Tecnológica

Yuri Dimitrov · The Ohio State University

Hi Jessica, Maybe try to find some meaning of the Caputo derivative at the initial point: aDa[f(a)] from the Mean-Value Theorem ( like Proposition 2... [more]

Hi Jessica, Maybe try to find some meaning of the Caputo derivative at the initial point: aDa[f(a)] from the Mean-Value Theorem ( like Proposition 2.2 in Fractional Taylor Series for Caputo Fractional Derivatives. Construction of Numerical Schemes by David Usero). If we let x->a in the mean value theorem we obtain a similar formula to the definition of classical derivatives. Another place to try is Geometric and Physical Interpretation of Fractional Integration and Fractional Diﬀerentiation by Igor Podlubny.

Following
Answer added to:
2 Convergence of an infinite series, each term of which is a product of two infinite cgt series. Product taken needs not be of consecutive terms.
By Arghya Bandyopadhyay · Khalisani College, Chandannagar

Arghya Bandyopadhyay · Khalisani College, Chandannagar

I should have posed the question differently, to make my point clear. Let sigma{an} and sigma{bn} be two given series, we can always form the double s... [more]

I should have posed the question differently, to make my point clear. Let sigma{an} and sigma{bn} be two given series, we can always form the double series sigmaf(m, n), where f(m, n) = ambn. For every arrangement g of f into a sequence G, we are led to a further series sigmaG(n) The convergence and sum of the series sigmaG(n) will depend on the arrangement of g. Different choices of g may yield different values of the product. But there is one very important case in which the terms f(m, n) are arranged diagonally to produce the Cauchy product and as @ Patrick_Sole has said the absolute convergence of series sigma(an) and sigma(bn) [ not the squared one, I think] implies convergence of the Cauchy product [ In fact Cauchy product arises quite naturally when we multiply two power series]. My point was about the other possible arrangement and their relation with convergence. I have simply no idea.... I would love no know on this.

Following

Topic Followers (494) See all

Ying Lai

Swiss Tropical and Public Health Institute
Joseph Quarcoo

American University of Nigeria
Hami Lagra

Université de Montpellier 2
Ashish Pathak

Sri Muthukumaran Institute of Technology
Simon Kristensen

Aarhus University
Oktay Duman

TOBB University of Economics and Technology
Serkan Demiriz

Gaziosmanpasa University
David Benko

University of South Alabama
Joe Diestel

University of Granada
Alexander Yu. Solynin

Texas Tech University

Real Analysis

Topic Followers (494) See all

Log in