Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1054.34008
Hsieh, Tsai-Ming; Lin, Shy-Der; Srivastava, H.M.
Some relationships between certain families of ordinary and fractional differential equations. (English)
[J] Comput. Math. Appl. 46, No. 10-11, 1483-1492 (2003). ISSN 0898-1221

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 2000:: *34A30 Linear ODE and systems
26A33 Fractional derivatives and integrals (real functions)

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]