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Erschienen in:
2017 | OriginalPaper | Buchkapitel
Operator Method for Constructing a Solution of a Class of Linear Differential Equations of Fractional Order
verfasst von : Batirkhan Kh. Turmetov
Erschienen in: Functional Analysis in Interdisciplinary Applications
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Abstract
In the paper certain method for constructing exact solutions of a class of linear differential equations of fractional order is considered. Algorithms for constructing solutions of the explicit form are developed for homogeneous and inhomogeneous differential equations of fractional order. This method is based on construction of normalized systems associated with fractional differentiation operator. 0 - normalized and f - normalized systems are built concerning to the pair of operators connected with the considered equation. Using 0 - normalized systems, linearly independent solutions of the homogeneous equation are constructed. Similarly, with the help of f - normalized systems partial solutions of the inhomogeneous equation are built in the case, where the right side is a quasi-polynomial, analytic function and an arbitrary function from the class of continuous functions.