Existence and uniqueness of solution for fractional differential equations with integral boundary conditions and the Adomian decomposition method

被引：4

作者：

Wanassi, Om Kalthoum ^{[1
,2
]}

Bourguiba, Rim ^{[2
]}

Torres, Delfim F. M. ^{[1
]}

机构：

[1] Univ Aveiro, Ctr Res & Dev Math & Applicat CIDMA, Dept Math, P-3810193 Aveiro, Portugal

[2] Univ Monastir, Fac Sci Monastir, LR18ES17, Monastir, Tunisia

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2024年 / 47卷 / 05期

关键词：

Adomian decomposition method; convergence analysis; error estimate; integral boundary conditions; nonlinear fractional differential equations; series solution; POSITIVE SOLUTIONS; SYSTEM;

D O I：

10.1002/mma.8880

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose an Adomian decomposition method to solve a class of nonlinear differential equations of fractional-order with modified Caputo derivatives and integral boundary conditions. Our approach uses the integral boundary conditions to derive an equivalent nonlinear Volterra integral equation before establishing existence and uniqueness of solution and a recursion scheme for the solution. The convergence of the method is proved and an error analysis given. Two numerical examples are solved by obtaining a rapidly converging sequence of analytical functions to the solution.

引用

页码：3582 / 3595

页数：14

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