Abstract
We are committed to the study of neutral type differential equation with delay and pairwise permutable matrices on Yang’s fractal sets \({\mathbb {R}}^{m\kappa } (0<\kappa \le 1, m\in {\mathbb {N}})\) 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.
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The work was partially supported by the National Natural Science Foundation of China (12001131), Supercomputing Algorithm and Application Laboratory of Guizhou University and Guian Scientific Innovation Company (No. K22-0116-003) and School-level project of Guizhou Education University (2020ZD008).
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Qiu, K., Wang, J. & Liao, Y. Representation of a Solution for a Neutral Type Differential Equation with Pure Delay on Fractal Sets. Qual. Theory Dyn. Syst. 22, 18 (2023). https://doi.org/10.1007/s12346-022-00712-9
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DOI: https://doi.org/10.1007/s12346-022-00712-9