Analytical solution of fractional variable order differential equations
The aim of the paper is to introduce and develop an approach for solving fractional variable order linear differential equations with different types of variable order derivative definitions (e.g. A-type, B-type, D-type, E-type), defined in previous works of the same authors. The introduced approach is motivated and based on switching schemes using fractional order transfer functions, that realize different types of variable order derivatives. The analytical solutions are obtained by using the Laplace transform and then are compared with numerical results, i.e. the methods are validated by comparison with numerical results. As the authors think the achieved methods can be helpful to validate existing or developed numerical algorithms for solving these types of equations.
scientific article; zbMATH DE number 6997518
scientific article