Maximal solutions to fractional differential equations
Copyright policy )Maximal solutions to fractional differential equations
Summary: When do fractional differential equations have maximal solutions? This note discusses this question in the following way. Firstly, a comparison theorem is formulated that involves fractional differential inequalities. Secondly, a sequence of approximative problems involving polynomials is analyzed, and it is shown that there is a subsequence of solutions whose limit is the maximal solution to the original problem of interest. In particular, the interval of existence for the maximal solution is the optimal length, aligning with best practice in the local theory of existence of solutions. We achieve this through an application of the Arzela-Ascoli theorem and our aforementioned comparison result. A YouTube video by the author designed to complement this work is available at \url{http://tinyurl.com/MaxFracDE}.
maximal solution, existence of solutions, fractional differential equations, Fractional ordinary differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, comparison theorem, initial value problem
maximal solution, existence of solutions, fractional differential equations, Fractional ordinary differential equations, Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations, comparison theorem, initial value problem
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