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On New Existence Results for Fractional Differential Equations in Quaternionic Analysis

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Abstract

In this paper, we establish sufficient conditions for the existence of solutions for the initial value problem of fractional differential equations. We consider the initial value problem in the space of Helmholtz-type generalized regular functions in the sense of quaternionic analysis. The results are obtained by the application of the method of associated spaces and the fixed point theorem. An example is provide to illustrate results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, PR China

    Zhan-Peng Yang & Tian-Zhou Xu

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  1. Zhan-Peng Yang
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  2. Tian-Zhou Xu
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Correspondence to Zhan-Peng Yang.

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Yang, ZP., Xu, TZ. On New Existence Results for Fractional Differential Equations in Quaternionic Analysis. Adv. Appl. Clifford Algebras 25, 733–740 (2015). https://doi.org/10.1007/s00006-014-0522-9

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  • DOI: https://doi.org/10.1007/s00006-014-0522-9

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