On Fractional Whittaker Equation and Operational Calculus
Vol. 20 (2013), No. 1, Page 127–146.
Rodrigues, M. M. ; Vieira, N.
On Fractional Whittaker Equation and Operational Calculus
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Abstract:
This paper is intended to investigate a fractional differential Whittaker's equation of order $2\alpha$, with $\alpha\in ]0, 1]$, involving the Riemann-Liouville derivative. We seek a possible solution in terms of power series by using operational approach for the Laplace and Mellin transform. A recurrence relation for coefficients is obtained. The existence and uniqueness of solutions is discussed via Banach fixed point theorem.
Keywords: Fractional differential equations, Riemann-Liouville derivative, Whittaker equation.
Mathematics Subject Classification (2010): Primary 35R11; Secondary 34B30, 42A38, 47H10.
Mathematical Reviews Number: MR3112089
Received: 2012-07-19
