Legendre fractional differential equation and Legender fractional polynomials
In this paper we study the Legender conformable fractional differential equation. It turns out that in certain cases, similar to the classical case, certain solutions are fractional polynomials. Further, we study basic properties of such fractional polynomials.
Keywords: Legendre Fractional Equation, Legendre Fractional Polynomials.
T. Abdeljawad. On conformable fractional calculus. Arxive math. To appear
R. Khalil, M. Al Horani, A. Yousef, and M. Sababheh. Anew definition of fractional derivative. Journal of computational applied mathematics, 264(2014)65-70.
Abu Hammad, M. and Khalil, R. Fractional Heat Equation. IJPAM. To appear.
K.S. Miller. An introduction to fractional calculus and fractional differential equations, J.Wiley, and Sons, New York 1993.
K. Oldham, and J. Spanier. The fractional calculus, theory and applications of differentiation and integration of arbitrary order. Academic Press, U.S.A. 1974
A.Kilbas, H. Srivastava, and J. Trujillo. Theory and applications of fractional differential equations. Math. Studies. Northholland, New York 2006.
I. Podlubny. Fractional differential equations. Academic Press, U.S.A. 1999.