This paper presents a chaotic jerk circuit model concerned with a stochastic fractal-fractional order α, β ∊ (0, 1] by adding external white noise to the input voltage. A new differentiation operator as the convolution of the power law is investigated. The new operators will be pointed to fractal-fractional differentiation and integration in the Riemann-Liouville (R-L) sense. Some sufficient conditions are achieved for the existence and uniqueness of solutions for considered framework by employing the Banach contraction principle. Finally, numerical simulation is provided to confirm the theoretical consequences.
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