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An efficient computational technique for local fractional Fokker Planck equation

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  • Singh, Jagdev
  • Jassim, Hassan Kamil
  • Kumar, Devendra

Abstract

The key aim of the present study is to compute the solution of local fractional Fokker Planck equation (LFFPE) on the Cantor set. We perform a comparison between the reduced differential transform method (RDTM) and local fractional series expansion method (LFSEM) employed to the LFFPE. The operators are considered in the local nature. The outcomes demonstrate the important characteristic of the two techniques which are very successful and simple to solve the differential equations having fractional derivative operator of local nature.

Suggested Citation

  • Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    • Handle: RePEc:eee:phsmap:v:555:y:2020:i:c:s0378437120302375
    DOI: 10.1016/j.physa.2020.124525
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    References listed on IDEAS

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    1. Hassan Kamil Jassim, 2015. "New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators," Journal of Mathematics, Hindawi, vol. 2015, pages 1-8, December.
    2. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, June.
    3. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    4. Shao-Hong Yan & Xiao-Hong Chen & Gong-Nan Xie & Carlo Cattani & Xiao-Jun Yang, 2014. "Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    5. Ai-Min Yang & Zeng-Shun Chen & H. M. Srivastava & Xiao-Jun Yang, 2013. "Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, November.
    6. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, January.
    7. Sheng-Ping Yan & Hossein Jafari & Hassan Kamil Jassim, 2014. "Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-7, June.
    8. Yong-Ju Yang & Dumitru Baleanu & Xiao-Jun Yang, 2013. "A Local Fractional Variational Iteration Method for Laplace Equation within Local Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, April.
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    Cited by:

    1. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Bezziou, Mohamed & Jebril, Iqbal & Dahmani, Zoubir, 2021. "A new nonlinear duffing system with sequential fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Abdel-Rehim, E.A. & Hassan, R.M. & El-Sayed, A.M.A., 2021. "On simulating the short and long memory of ergodic Markov and Non-Markov genetic diffusion processes on the long run," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Muath Awadalla & Kinda Abuasbeh & Muthaiah Subramanian & Murugesan Manigandan, 2022. "On a System of ψ -Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions," Mathematics, MDPI, vol. 10(10), pages 1-15, May.
    6. Hassan Kamil Jassim & Mohammed Abdulshareef Hussein, 2023. "A New Approach for Solving Nonlinear Fractional Ordinary Differential Equations," Mathematics, MDPI, vol. 11(7), pages 1-13, March.
    7. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    8. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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