[PDF] Existence and Uniqueness Theorems for Differential Equations with Proportional Delay-论文阅读讨论-ReadPaper

摘要

The differential equation (DE) with proportional delay is a particular caseof the time-dependent delay differential equation (DDE). In this paper, wesolve non-linear DEs with proportional delay using the successive approximationmethod (SAM). We prove the existence, uniqueness of theorems, and stability forDEs with proportional delay using SAM. We derive convergence results for theseequations by using the Lipschitz condition. We generalize these results to thefractional differential equations (FDEs) and system of FDEs containing Caputofractional derivative. Further, we obtain the series solution of the pantographequation and Ambartsumian equation in the form of a power series which areconvergent for all reals. Finally, we illustrate the efficacy of the SAM byexample. The results obtained by SAM are compared with exact solutions andother iterative methods. It is observed that SAM is simpler compared to othermethods and the solutions obtained using SAM are consistent with the exactsolution.

展开全部

图表提取

论文十问

参考文献

被引用

提问与回答

暂无人提供速读十问回答