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Explicit solutions of Jacobi and Gauss differential equations by means of operators of fractional calculus. (English) Zbl 1151.34003
This paper is concerned with the use of methods from the fractional calculus to solve integer-order differential equations. Following preliminaries, in which basic ideas from the fractional calculus are introduced, the authors go on to present a new theorem on solutions of integer-order problems based on an existing theorem by Tu, Chyan and Srivastava for fractional order equations. This new result provides alternative formulations of solutions of classical differential equations.
MSC:
34A05Methods of solution of ODE
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
26A33Fractional derivatives and integrals (real functions)