2014/07/31 by Iftikhar Ali, Ali, Iftikhar, B. Chanane +3
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.1408.2783
openalex publication_date 2014/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a time fractional differential equation of order \α,\n0<\α<1,
frac
partial c(x,t)
partial\nt=C0
mathcalDt
alpha[(Ac)(x,t)]+q(x,t) ,
quad x gt; 0, t gt; 0,
quad\nc(x,0)=f(x). where C0\Dt\α is the Caputo fractional\nderivative of order \α, A is a linear differential operator, q(x,t)\nis a source term, and f(x) is the inital condition. Approximate (truncated)\nseries solutions are obtained by means of the Variational Iteration Method\n(VIM). We find the series solutions for different cases of the source term, in\na form that is readily implementable on the computer where symbolic computation\nplatform is available. The error in truncated solution cn diminishes\nexponentially fast for a given \α as the number of terms in the series\nincreases. VIM has several advantages over other methods that produce solutions\nin the series form. The truncated VIM solutions often converge rapidly\nrequiring only a few terms for fast and accurate approximations.\n