Abstract:
Numerical calculation of the fractional integrals and derivatives is the code to
search fractional calculus and solve fractional differential equations. The exact
solutions to fractional differential equations are compelling to get in real applications, due to the nonlocality and complexity of the fractional differential
operators, especially for variable-order fractional differential equations. Therefore, it is significant to enhance numerical methods for fractional differential
equations. In this work, we consider variable-order fractional differential equations by reproducing kernel method. There has been much attention in the
use of reproducing kernels for the solutions to many problems in the recent
years. We give an example to demonstrate how efficiently our theory can be
implemented in practice.