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Abstract
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Stochastic equations are powerful mathematical tools used to study systems having random effects. The current manuscript studies the two distinct systems: the stochastic conformable Zakharov system (SCZs) and stochastic conformable Hirota-Macari system (SCHMs) with multiplicative noises. Both systems are investigated using the conformable derivative in terms of stratonovich formulation. These systems are chosen for study due to their relevance and significance in understanding the behavior of complex physical phenomena influenced by stochastic effect. The novelty lies in the applications of the unified solver method, which is a succinct, direct and efficient technique for obtaining solutions in rational, trigonometric and hyperbolic forms. To demonstrate the effect of multiplicative noise and conformable derivative on the solutions of SCZs and SCHMs, 3D and 2D graphs are illustrated by using Mathematica 11. Our findings highlight the sustaining role of the multiplicative noise, which stabilizes the solutions of systems around zero. Overall, this study deepens the understanding of the interaction between stochastic effects and conformable derivatives in the context of these complex systems.
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