Homotopy analysis method and its application for solving integro-di erential equations of fractional order
Publish Year: 1397
نوع سند: مقاله کنفرانسی
زبان: English
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شناسه ملی سند علمی:
IDS03_051
تاریخ نمایه سازی: 31 اردیبهشت 1398
Abstract:
In this paper, based on the homotopy analysis method (HAM), a analytical technique is proposed to solve nonlinear fractional integro-di erential equa- tions (FIDEs). Di erent from all other analytical methods, it provides a simple way to adjust and control the convergence region of series solution by introducing an auxiliary parameter ~. This work illustrates the valid- ity and high accuracy of the homotopy analysis method for the non-linear integro-di erential equations with fractional order. The basic concepts of the HAM can be widely used to solve other strongly non-linear fractional problems. Several numerical examples are given to illustrate the convergence of approximate solutions to analytical solutions. The comparison of the re- sults obtained by the HAM with the exact solutions show that the HAM is very e ective and simple for solving various linear and nonlinear fractional problems.
Keywords:
Homotopy analysis method , Fractional integro-di erential equation , Series solution , Approximate analytical solutions , Caputo fractional derivative
Authors
Hussein Sahihi
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Saeid Abbasbandy
Department of Mathematics, Imam Khomeini International University, Qazvin ۳۴۱۴۹, Iran