An algebraic derivative associated to the operator D δ

V. Almeida; N. Castro; J. Rodríguez

Banach Center Publications (2000)

  • Volume: 53, Issue: 1, page 71-78
  • ISSN: 0137-6934

Abstract

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In this paper we get an algebraic derivative relative to the convolution ( f * g ) ( t ) = ∫ 0 t i f ( t - ψ ) g ( ψ ) d ψ associated to the operator D δ , which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation

How to cite

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Almeida, V., Castro, N., and Rodríguez, J.. "An algebraic derivative associated to the operator $D^δ$." Banach Center Publications 53.1 (2000): 71-78. <http://eudml.org/doc/209078>.

@article{Almeida2000,
abstract = {In this paper we get an algebraic derivative relative to the convolution $(f*g)(t)=∫_0^ti f(t-ψ)g(ψ)dψ$ associated to the operator $D^δ$, which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation},
author = {Almeida, V., Castro, N., Rodríguez, J.},
journal = {Banach Center Publications},
keywords = {Riemann-Liouville fractional integral operator; Mikusiński operational calculus; algebraic derivative; convolution; integral-differential equation},
language = {eng},
number = {1},
pages = {71-78},
title = {An algebraic derivative associated to the operator $D^δ$},
url = {http://eudml.org/doc/209078},
volume = {53},
year = {2000},
}

TY - JOUR
AU - Almeida, V.
AU - Castro, N.
AU - Rodríguez, J.
TI - An algebraic derivative associated to the operator $D^δ$
JO - Banach Center Publications
PY - 2000
VL - 53
IS - 1
SP - 71
EP - 78
AB - In this paper we get an algebraic derivative relative to the convolution $(f*g)(t)=∫_0^ti f(t-ψ)g(ψ)dψ$ associated to the operator $D^δ$, which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation
LA - eng
KW - Riemann-Liouville fractional integral operator; Mikusiński operational calculus; algebraic derivative; convolution; integral-differential equation
UR - http://eudml.org/doc/209078
ER -

References

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  1. [1] J. A. Alamo and J. Rodríguez, Cálculo operacional de Mikusiński para el operador de Riemann-Liouville y su generalizado, Rev. Acad. Canar. Cienc. 1 (1993), 31-40. 
  2. [2] W. Kierat and K. Skórnik, A remark on solutions of the Laguerre differential equation, Integral Transforms and Special Functions 1 (1993), 315-316. Zbl0827.44003
  3. [3] J. Mikusiński, Operational Calculus, Pergamon, Oxford, 1959. 
  4. [4] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood, 1984. Zbl0535.33001
  5. [5] Y K. Yosida, Operational Calculus. A Theory of Hyperfunctions, Springer-Verlag, New York, 1984. 

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