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Fractal-view analysis of local fractional Fokker–Planck equation occurring in modelling of particle’s Brownian motion

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Abstract

In this paper, the solution and behaviour of local fractional Fokker–Planck equation (LFFPE) is investigated in fractal media. For this purpose, the local fractional homotopy perturbation Elzaki transform method (LFHPETM) is proposed and utilized to explore the solution of LFFPE. The proposed scheme is a merger of well known local fractional homotopy perturbation technique and recently introduced local fractional Elzaki transform (LFET). The convergence and uniqueness analyses for LFHPETM solution of the general partial differential equation is also presented along with the computational procedure of this new hybrid combination. Three examples of LFFPE are illustrated to depict the applicability of the employed method with graphical simulations on Cantor set. The copulation of LFET with local fractional homotopy perturbation method (LFHPM) efficiently provides the faster solution for LFFPE in a fractal domain as compared to the LFHPM. Furthermore, the achieved solutions are also in a good match with existing solutions. The 3D behavior of solutions of LFFPEs are presented for fractal order \(\ln 2/\ln 3\). Figures illustrate the 3D surface graphics of solutions with respect to input variables.

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Authors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, 303905, India

    Jagdev Singh

  2. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Jagdev Singh & Dumitru Baleanu

  3. Department of BCA, L.N.D. College, B.R. Ambedkar Bihar University, Muzaffarpur, Motihari, Bihar, 845401, India

    Ved Prakash Dubey

  4. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, 302004, India

    Devendra Kumar

  5. Department of Physics, L.N.D. College, B.R. Ambedkar Bihar University, Muzaffarpur, Motihari, Bihar, 845401, India

    Sarvesh Dubey

  6. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

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Correspondence to Devendra Kumar.

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Singh, J., Dubey, V.P., Kumar, D. et al. Fractal-view analysis of local fractional Fokker–Planck equation occurring in modelling of particle’s Brownian motion. Opt Quant Electron 56, 1109 (2024). https://doi.org/10.1007/s11082-024-06842-5

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