# An algebraic derivative associated to the operator ${D}^{\delta}$

V. Almeida; N. Castro; J. Rodríguez

Banach Center Publications (2000)

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

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topAlmeida, 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

top- [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] 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] J. Mikusiński, Operational Calculus, Pergamon, Oxford, 1959.
- [4] H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood, 1984. Zbl0535.33001
- [5] Y K. Yosida, Operational Calculus. A Theory of Hyperfunctions, Springer-Verlag, New York, 1984.

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