Abstract
This work considers numerical solutions of variable fractional order, multi-term differential equations. A second order numerical approach has been used here to approximate fractional order derivative and this approach is similar to the fractional-variable order derivative approach for single-term case (see Cao and Qiu (Appl. Math. Lett. 61, 88–94, 2016)). To construct a multi-term, fractional-variable order differential equation, we first add y(t) term to the single-term equation and then test the convergency of the method. Secondly, we add a second order ordinary derivative term to the equation and this term is approximated by central finite differences, where the variable Riemann–Liouville derivative approximation is based on the shifted GrÜnwald approximation technique and the numerical scheme is still convergent.
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Ayaz, F., Güner, İ.B. (2020). A Numerical Approach for Variable Order Fractional Equations. In: Machado, J., Özdemir, N., Baleanu, D. (eds) Numerical Solutions of Realistic Nonlinear Phenomena. Nonlinear Systems and Complexity, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-030-37141-8_11
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