This article is devoted to establish the existence of solution of $\left(\alpha ,\beta \right)$-order coupled implicit fractional differential equation with initial conditions, using Laplace transform method. The topological degree theory is used to obtain sufficient conditions for uniqueness and at least one solution of the considered system. Beside this, Ulam’s type stabilities are discussed for the proposed system. To support our main results, we present an example.

中文翻译：

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（α，β）阶耦合隐Caputo分数阶微分方程的拓扑度分析

本文致力于建立解的存在性 $（\alpha ，\beta ）$拉普拉斯变换法求解具有初始条件的二阶隐式分数阶微分方程。拓扑度理论用于获得唯一性的充分条件和所考虑系统的至少一种解决方案。除此之外，还针对所提议的系统讨论了Ulam的类型稳定性。为了支持我们的主要结果，我们举一个例子。