Abstract. We introduce a special type of ordinary differential equations d α(t)x/dtα(t) = f(t, x(t)) whose order of differentiation is a continuous function depending on the independent variable t. We show that such dynamical order of differentiation equations (DODE) can be solved as a Volterra integral equations of second kind with singular integrable kernel. We find the conditions for existence and uniqueness of solutions of such DODE. We present the numeric approach and solutions for particular cases for α(t) ∈ (0, 2) and discuss the asymptotic approach of the DODE solutions towards the classical ODE solutions for α = 1 and 2.
Electronic Journal of Differential Equations
Department of Mathematics Texas State University
International Conference on Applications of Mathematics to Nonlinear Sciences
Number of Pages
Scholarly Commons Citation
Ludu, A., & Khanal, H. (2017). Differential Equations of Dynamical Order. Electronic Journal of Differential Equations, Conference 24((2017)). Retrieved from https://commons.erau.edu/publication/1311