A semi-analytic method with an effect of memory for solving fractional differential equations

Advances in Difference Equations

Kyunghoon Kim¹  Bongsoo Jang¹ 

[1] Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan, Republic of Korea

关键词: Fractional Order;    Fractional Derivative;    Recursive Relation;    Fractional Differential Equation;    Homotopy Analysis Method;   

DOI  :  10.1186/1687-1847-2013-371

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose a new modification of the multistage generalized differential transform method (MsGDTM) for solving fractional differential equations. In MsGDTM, it is the key how to impose an initial condition in each sub-domain to obtain an accurate approximate solution. In several literature works (Odibat et al. in Comput. Math. Appl. 59:1462-1472, 2010; Alomari in Comput. Math. Appl. 61:2528-2534, 2011; Gökdoğan et al. in Math. Comput. Model. 54:2132-2138, 2011), authors have updated an initial condition in each sub-domain by using the approximate solution in the previous sub-domain. However, we point out that this approach is hard to apply an effect of memory which is the basic property of fractional differential equations. Here we provide a new algorithm to impose the initial conditions by using the integral operator that enhances accuracy. Several illustrative examples are demonstrated, and it is shown that the proposed technique is robust and accurate for solving fractional differential equations.

【 授权许可】

CC BY