Resumen de Representation of a Solution for a Neutral Type Differential Equation with Pure Delay on Fractal Sets

Kee Qiu, JinRong Wang, Yumei Liao

• We are committed to the study of neutral type differential equation with delay and pairwise permutable matrices on Yang’s fractal sets Rmκ (0 < κ ≤ 1, m ∈ N) via local fractional-order calculus theory. Firstly, the fundamental solution of the matrix equation with initial condition has been presented by constructing the piecewise defined delayed matrix polynomial function on Yang’s fractal sets. Secondly, assuming the linear parts to be given by pairwise permutable constant matrices, we got the exact solution of the homogeneous initial value problem and the non-homogeneous neutral differential equation with a given initial condition. Finally, the solution of a neutral differential equation with pure delay was given by the sum of solution of homogeneous problem and a particular solution of non-homogeneous problem. The present formulation can lay a foundation for the study of system stability, controllability and oscillatory