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The main aim of this investigation is to establish the weighted Simpson-like type identity and related variants for a mapping for which the power of the absolute of the first derivative is s-preinvex. By considering this identity, numerous novel weighted Simpson’s like type and related estimation type results for bounded first order differentiable functions are apprehended. Several notable results can be obtained as consequences for the suitable selection of n and !: Meanwhile, the results are illustrated with two special functions involving modified Bessel function and q-digamma function to obtain the efficiency and supremacy of the proposed technique for many problems of wave propagation and static potentials.