On solutions of variable-order fractional differential equations

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.