Left and Right Riemann-Liouville Fractional Derivatives Fractional Differential Equation Euler-Lagrange Equation Variational Principle 26A33 70H03 70S05 49S05 70H25
Issue Date:
2007
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Fractional Calculus and Applied Analysis, Vol. 10, No 2, (2007), 139p-150p
Abstract:
We treat the fractional order differential equation that contains the left
and right Riemann-Liouville fractional derivatives. Such equations arise as
the Euler-Lagrange equation in variational principles with fractional derivatives.
We reduce the problem to a Fredholm integral equation and construct
a solution in the space of continuous functions. Two competing approaches
in formulating differential equations of fractional order in Mechanics and
Physics are compared in a specific example. It is concluded that only the
physical interpretation of the problem can give a clue which approach should
be taken.