Abstract The aim of this article is to form new existence theory for global solutions to nonlinear fractional differential equations. Traditional approaches to existence, uniqueness and approximation of global solutions for initial value problems involving fractional differential equations have been unwieldy or intractable due to the limitations of previously used methods. This includes, for example, certain invariance conditions of the underlying local fixed point strategies. Herein we draw on an alternative tactics, applying the more modern ideas of continuation methods for contractive maps to fractional differential equations. In doing so, we shed new light on the situation, producing these new perspectives through a range of novel theorems that involve sufficient conditions under which global existence, uniqueness, approximation and location of solutions are ensured.

中文翻译：

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分数阶微分方程的全局存在理论：收缩映射连续法的新进展

摘要 本文旨在形成非线性分数阶微分方程全局解的新存在理论。由于先前使用的方法的局限性，涉及分数阶微分方程的初始值问题的全局解的存在性、唯一性和近似值的传统方法变得笨拙或难以处理。例如，这包括潜在局部定点策略的某些不变性条件。在这里，我们采用了一种替代策略，将更现代的用于收缩映射的延拓方法的思想应用于分数微分方程。在这样做的过程中，我们对这种情况有了新的认识，通过一系列新的定理产生了这些新的观点，这些定理涉及充分条件，在这些条件下，全局存在、唯一性、