Sabir, ZulqurnainWahab, Hafiz AbdulNguyen, Tri GiaAltamirano, Gilder CiezaErdogan, FevziAli, Mohamed R.2025-05-102025-05-1020221432-76431433-747910.1007/s00500-022-07065-02-s2.0-85128771480https://doi.org/10.1007/s00500-022-07065-0https://hdl.handle.net/20.500.14720/14087Ali, Mohamed/0000-0002-0795-0709; Sabir, Zulqurnain/0000-0001-7466-6233; Cieza Altamirano, Gilder/0000-0002-7936-1495The purpose of this study is to introduce a stochastic computing solver for the multi-pantograph delay differential equation (MP-DDE). The MP-DDE is not easy to solve due to the singularities and pantograph terms. An advance computational intelligent paradigm is proposed to solve MP-DDE of the second kind by manipulating the procedures of the artificial neural networks (ANNs) through the optimization of genetic algorithm (GA) and sequential quadratic programming (SQP), i.e., ANNs-GA-SQP. A fitness function is constructed based on MP-DDE of second kind and corresponding boundary conditions. The correctness of the ANNs-GA-SQP is observed by performing the comparison of the proposed and exact solutions. The values of the absolute error (AE) in good measures are provided to solve the MP-DDE of the second kind. The efficacy and correctness of the stochastic computing approach to solve three problems of the MP-DDE of second kind to signify the efficiency, worth, and consistency. Moreover, the statistical soundings are applied to validate the accuracy and consistency.eninfo:eu-repo/semantics/closedAccessPantographStochastic ComputingArtificial IntelligenceStatistical SoundingsGlobal SchemeSingular SystemsLocal Search SchemeArticle2614Q2Q167016713WOS:000786726200002