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G-Meijer functions series as solutions for some Euler-Lagrange equations of fractional mechanics

Fractional oscillator problem on a finite time interval is studied. This equation obtained by minimum action principle contains left- and right-sided fractional derivatives. Mellin transform is applied and general continuous solution in form of G-Meijer functions series is derived for order alpha - an irrational number. Solutions of fractional oscillator equation derived using Mellin transform are compared with that obtained via Banach theorem on a fixed point. As a result analytical relations for certain iterated fractional integrals appear. These integrals will be applied in solving a general class of variational fractional equations.
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