In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging.

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<abstract> <p>In this paper, a numerical method to solve a class of stochastic nonlinear differential equations is introduced. The proposed method is based on the Temimi-Ansari method. The special states of the four systems are studied to show that the proposed method is efficient and applicable. These systems are stochastic Langevin's equation, Ginzburg-Landau equation, Davis-Skodje, and Brusselator systems. The results clarify the accuracy and efficacy of the presented new method with no need for any restrictive assumptions for nonlinear terms.</p> </abstract>

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