Numerical Solution of Variable-Order Fractional Differential Equations Using Bernoulli Polynomials

  title={Numerical Solution of Variable-Order Fractional Differential Equations Using Bernoulli Polynomials},
  author={Somayeh Nemati and Pedro Miguel Lima and Delfim F. M. Torres},
We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the Riemann–Liouville integral operator was used to give approximations for the unknown function and its variable-order derivatives. An operational matrix of variable-order fractional integration was introduced for the Bernoulli functions. By assuming that the solution of… 

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