Abstract
Fractional integrals and derivatives in the operational calculus of generalized functions are interpreted as solutions of algebraic differential equations. This yields a transcendental characterization which then leads to a new concept of logarithms for operators.
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References
Mikusiński, Jan, Operational Calculus, Pergamon Press, London, 1959.
Erdélyi, Arthur, Operational Calculus and Generalized Functions, Holt, Rinehart and Winston, New York, 1962.
Mikusiński, Jan, "Remarks on the algebraic derivative in the Operational Calculus," Studia Math., 19(1960), 187–192.
Gesztelyi, Erno, "Anwendung der Operatorenrechnung auf lineare Differentialgleichungen mit Polynom-Koeffizienten," Publ. Math. Debrecen, 10(1963), 215–243.
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© 1975 Springer-Verlag
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Struble, R.A. (1975). Fractional calculus in the operator field of generalized functions. In: Ross, B. (eds) Fractional Calculus and Its Applications. Lecture Notes in Mathematics, vol 457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067114
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DOI: https://doi.org/10.1007/BFb0067114
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