Complex variable approach to analysis of a fractional differential equation in the real line

Müfit Şan

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arXiv · 1706.08916

Complex variable approach to analysis of a fractional differential equation in the real line

Müfit Şan

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Abstract

The first aim of this work is to establish a Peano type existence theorem for an initial value problem involving complex fractional derivative and the second is, as a consequence of this theorem, to give a partial answer to the local existence of the continuous solution for the following problem with Riemann-Liouville fractional derivative: \begin{equation*} \begin{cases} &D^{q}u(x) = f\big(x,u(x)\big), \\ &u(0)=b, \ \ \ (b\neq 0). \\ \end{cases} \end{equation*} Moreover, in the special cases of considered problem, we investigate some geometric properties of the solutions.

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Müfit Şan. 2017-06-27. Complex variable approach to analysis of a fractional differential equation in the real line. https://arxiv.org/abs/1706.08916

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