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Numerical analysis nonlinear multi‐term time fractional differential equation with collocation method via fractional B‐spline
Author(s) -
Ramezani Mohammad
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5642
Subject(s) - mathematics , collocation method , nonlinear system , fractional calculus , collocation (remote sensing) , differential equation , mathematical analysis , numerical analysis , term (time) , orthogonal collocation , b spline , ordinary differential equation , computer science , physics , quantum mechanics , machine learning
In this work, we present numerical analysis for nonlinear multi‐term time fractional differential equation which involve Caputo‐type fractional derivatives for 0 < α i < 1 , i = 1 , 2 , ⋯ , N . The proposed method is based on utilization of fractional B‐spline basics in collocation method. The scheme can be readily obtained efficient and quite accurate with less computational work numerical result. The proposal approach transform nonlinear multi‐term time fractional differential equation into a suitable linear system of algebraic equations which can be solved by a suitable numerical method. The numerical experiments will be verify to demonstrate the effectiveness of our method for solving one‐ and two‐dimensional multi‐term time fractional differential equation.