Submitting Campus

Daytona Beach

Department

Mathematics

Document Type

Conference Proceeding

Publication/Presentation Date

Winter 11-15-2017

Abstract/Description

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.

Publication Title

Electronic Journal of Differential Equations

Publisher

Department of Mathematics Texas State University

Paper Number

47-61

Number of Pages

14

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