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The use of fractional B-splines wavelets in multiterms fractional ordinary differential equations. (English) Zbl 1207.34009

Summary: We discuss the existence and uniqueness of solutions of nonhomogeneous linear differential equations of arbitrary positive real order by using fractional B-Spline wavelets and the Mittag-Leffler function. The differential operators are taken in the Riemann-Liouville sense and the initial values are zero. A scheme for solving the fractional differential equations and an explicit expression of the solution is given in this paper. At last, we present the asymptotic solution of the differential equations of fractional order and the corresponding truncated error.

MSC:

34A08 Fractional ordinary differential equations
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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References:

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