We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value problem under consideration, and give necessary and sufficient conditions for the existence of solutions. The obtained theoretical results are confirmed by a model example.

翻译：我们使用数字分析技术来构建一系列连续近似,以在符合迪里赫莱特边界条件的情况下解决分差方程式的解决方案。 我们证明近差法序列与极限函数一致,这是所考虑的边界价值问题的独特解决办法,并为解决方案的存在提供了必要和充分的条件。 获得的理论结果得到了一个范例的证实。