Numerical solution of distributed order fractional differential equations. (English) Zbl 1349.65212
Summary: In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
| 34K37 | Functional-differential equations with fractional derivatives |
| 65D30 | Numerical integration |
Keywords:
distributed order differential equation; multi-term fractional differential equation; numerical solution; analog equation methodReferences:
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