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Explicit solutions of some linear ordinary and partial fractional differintegral equations. (English) Zbl 1033.45006

The authors employ some general theorems and lemmas, related to fractional differintegrals (fractional differential and integral operators), to obtain (in a unified manner) particular solutions of second and third order homogeneous and non-homogeneous linear ordinary fractional differintegral equations and some partial fractional differintegral equations. They predict some interesting consequences and applications of their results.

In addition to the references cited by them, following reference (from the point of view of applications of fractional differintegrals) may be of interest: P. K. Banerji and A. M. H. Alhashemi [Proc. Natl. Acad. Sci. India, Sect. A 69, 191–197 (1999; Zbl 0965.34073); J. Indian Acad. Math. 21, 155–167 (1999; Zbl 0994.34002)]; Y. Deora and P. K. Banerji [Fractional Calc. 5, 91–94 (1994; Zbl 0814.35089)].

MSC:
45J05Integro-ordinary differential equations
45K05Integro-partial differential equations
26A33Fractional derivatives and integrals (real functions)