THEORETICAL PREDICTIONS OF EXISTENCE AND UNIQUENESS FOR STOCHASTIC M-FRACTIONAL DIFFERENTIAL MODELS OF RANDOM BROWNIAN MOTION, EXHIBITED WITH MATRIX SPECTRAL COLLOCATION SOLUTIONS AND SIMULATED WITH THE ELECTRICAL ENGINEERING RLC UTILITY AS A CASE INTERPRETATION

Abstract

Within this analysis, our findings are classified into two main features. In the first one, theoretical aspects, including the EUP of fractional SDMs of [Formula: see text]-derivative sense, where the standard Brownian motion represents the stochastic term, are debated. We utilize SIPT and construct suitable hypotheses to prove the existence of an invariant point to a welldefined operator built on a Banach space. In the other feature, the SL-SCM based on matrix representations of the truncated Legendre series and its fractional derivative is employed to obtain approximate realizations for the exact paths of the stochastic processes that satisfy the given constraints. Accordingly, a simulation technique to obtain the approximated values of the white noise of the Gaussian type is discussed, and suitable node points are used. Hereafter, assuming the smoothness of the solution, the convergence prediction of the suggested framework is elucidated, and the Legendre convergence rate is investigated. For a novel in-depth analysis and to match the actual behavior of randomness, Itô’s stochastic calculus is utilized to analyze the noise in electrical circuits by showcasing the SRLCU as a case interpretation for the first time. Furthermore, other examples of contrasting types are performed to illustrate the reliability and consistency of the obtained theoretical consequences and the accuracy of the utilized spectral method. Throughout the discussion, various arguments, data, and charts are debated. In the end, highlights and remarks that reflect the paper’s contents are talk.

Topics & Concepts