An efficient iterative method for multi-order nonlinear fractional differential equations based on the integrated Bernoulli polynomials. (English) Zbl 07830978
Summary: We present an effective practical approach for solving multi-order nonlinear fractional differential equations. Our method uses integrated Bernoulli polynomials and comes with a comprehensive convergence analysis. The integrated Bernoulli polynomials are combined with the collocation and simple iteration methods to approximate the solutions. We have provided several numerical examples to demonstrate the effectiveness, strength, and flexibility of our method. The results obtained from implementing the method have been compared with exact solutions and results obtained from other methods mentioned in the articles.
MSC:
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 26A33 | Fractional derivatives and integrals |
| 34L30 | Nonlinear ordinary differential operators |
| 33F05 | Numerical approximation and evaluation of special functions |
| 41A10 | Approximation by polynomials |
Keywords:
multi-order nonlinear fractional differential equation; integrated Bernoulli polynomials; iterative method; convergence analysisReferences:
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