%0 Journal Article
%T Symplectic Newton–Cotes product Integration methods for fractional Hamiltonian systems
%A Tiwari, Shruti 
%J Indian Journal of Mathematics
%V 67
%N 1
%D 2025
%P 39–60
%@ 0019-5324
%I The Allahabad Mathematical Society
%K Fractional Hamiltonian systems, Caputo fractional derivatives, Symplectic integrators, Closed Newton–Cotes product integration, Sum-of-exponentials history compression
%X This work presents a novel class of composite product-integration closed Newton--Cotes (CNC) integrators specifically designed for Hamiltonian systems governed by Caputo fractional derivatives of order $1 < \alpha < 2$. The proposed methodology establishes explicit full-history convolution weights while constructing a discrete variational principle within an extended phase space, ultimately yielding a symplectic mapping. Through rigorous analysis, we demonstrate global error bounds of $O(h^{2-\alpha})$ for CNC-2 and $O(h^{4-\alpha})$ for CNC-4 under conventional regularity assumptions. The linear stability characteristics are analyzed via the generating function of convolution weights, while long-term energy drift behavior is quantified. Additionally, efficient implementation strategies are developed that achieve $O(1)$ per-step computational complexity through systematic history truncation and sum-of-exponentials compression techniques. Comprehensive numerical experiments validate the theoretical 
   predictions and demonstrate superior performance relative to existing fractional integrators.