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**Some relationships between certain families of ordinary and fractional differential equations.**
*(English)*
Zbl 1054.34008

Summary: In recent years, many authors demonstrated the usefulness of fractional calculus operators in the derivation of (explicit) particular solutions of a number of linear ordinary and partial differential equations of second and higher order. In particular, by making use of the operators of fractional calculus based upon the Cauchy-Goursat integral formula, a certain family of nearly-simple harmonic vibration equations was considered systematically in a series of papers which appeared quite recently. The main object of the present sequel to all these earlier works is to investigate some relationships between such families of fractional differential equations and certain classes of ordinary differential equations. A preliminary interpretation of this family of nearly-simple harmonic vibration equations by means of an example involving linear electric circuits is provided, too.

### MSC:

34A30 | Linear ordinary differential equations and systems |

26A33 | Fractional derivatives and integrals |

### Keywords:

Fractional calculus; Cauchy-Goursat integral formula; Principal value; Generalized Leibniz rule; Analytic functions; Differintegral equations; Index law; Linearity property; Fuchsian (and non-Fuchsian) differential equations; Simple harmonic vibration equations; Nearly-simple harmonic vibration equations; Linear electric circuits; Fractional differential equations; constant coefficients
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\textit{T.-M. Hsieh} et al., Comput. Math. Appl. 46, No. 10--11, 1483--1492 (2003; Zbl 1054.34008)

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DOI

### References:

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