Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Fractional Hamiltonian analysis of irregular systems
Signal Processing - Fractional calculus applications in signals and systems
Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering
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An equation with the antisymmetric fractional derivative of order @a@?(1,2), containing the t^@b-potential is solved using the Mellin transform method. The solutions are analogues of exponential functions of a new type. They are represented as Meijer G-function series in a finite time interval. In the classical limit @a@?1^+, the eigenfunction equation for a derivative of the first order and its solution-an exponential function, are recovered. Then an analogy between the derivation of Euler-Lagrange equations in fractional mechanics and in classical mechanics is discussed. The results are applied to a simple fractional Euler-Lagrange equation containing an antisymmetric fractional derivative and its general solution is obtained.