Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900788 | Applied Mathematics and Computation | 2018 | 14 Pages |
Abstract
f(x)=âj=0mcjα,Ï(xÏâaÏ)jα+em(x)with mâN0,cjα,ÏâR,xâ¯>â¯aâ¯>â¯0 and 0â¯<â¯Î±â¯â¤â¯1. In case Ï=α=1, this expression coincides with the classical Taylor formula. The coefficients cjα,Ï,j=0,â¦,m as well as the residual term em(x) are given in terms of the generalized Caputo-type fractional derivatives. Several examples and applications of these results for the approximation of functions and for solving some fractional differential equations in series form are given in illustration.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mondher Benjemaa,