BULLETIN of the

POLISH ACADEMY of SCIENCES

TECHNICAL SCIENCES

BULLETIN of the POLISH ACADEMY of SCIENCES: TECHNICAL SCIENCES
Volume 58, Issue 4, December 2010

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pp 573 - 581

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Existence - uniqueness result for a certain equation of motion in fractional mechanics

M. KLIMEK
The eigenfunction equation of fractional variational operator including left and right derivative of order α is solved using the fixed point theorem. Its exact and approximate solutions are studied in detail. The corresponding boundary conditions are derived by means of the composition rules of fractional operators and the theorem on a unique particular solution of the considered fractional differential equation is proved
Key words:

fractional derivative, fractional differential equation, Euler-Lagrange equation, fixed point theorem, approximate solution


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