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Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique

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  • Dubey, Ved Prakash
  • Singh, Jagdev
  • Alshehri, Ahmed M.
  • Dubey, Sarvesh
  • Kumar, Devendra

Abstract

In this paper, we present an efficient computational approach named as Sumudu residual power series method (SRPSM) to solve fractional Bloch equations appearing in an NMR flow. This method is a copulation of the residual power series method (RPSM) and the Sumudu transform to construct approximate solution in shapes of sharp convergent series by adopting the notion of limit with a view of smooth calculations and time saving strategy as compared to the classical RPSM in which computations of fractional derivatives are required. This work also verifies and compares the solution obtained by the proposed technique with the classical RPSM. To assure the applicability, performance, and reliability of the introduced method, a system of fractional Bloch equations are examined along with numerical simulations. The aspect of application supported with computer simulations demonstrates that the suggested approach is precise, and appropriate to explore the solutions of linear & nonlinear initial value problems with fractional-order derivatives.

Suggested Citation

  • Dubey, Ved Prakash & Singh, Jagdev & Alshehri, Ahmed M. & Dubey, Sarvesh & Kumar, Devendra, 2022. "Forecasting the behavior of fractional order Bloch equations appearing in NMR flow via a hybrid computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008700
    DOI: 10.1016/j.chaos.2022.112691
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    References listed on IDEAS

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    1. Eriqat, Tareq & El-Ajou, Ahmad & Oqielat, Moa'ath N. & Al-Zhour, Zeyad & Momani, Shaher, 2020. "A New Attractive Analytic Approach for Solutions of Linear and Nonlinear Neutral Fractional Pantograph Equations," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, July.
    3. Fethi Bin Muhammed Belgacem & Ahmed Abdullatif Karaballi, 2006. "Sumudu transform fundamental properties investigations and applications," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-23, May.
    4. H. M. Srivastava & Alireza Khalili Golmankhaneh & Dumitru Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    5. Dubey, Ved Prakash & Kumar, Rajnesh & Kumar, Devendra, 2019. "A reliable treatment of residual power series method for time-fractional Black–Scholes European option pricing equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    6. Omar Abu Arqub & Zaer Abo-Hammour & Ramzi Al-Badarneh & Shaher Momani, 2013. "A Reliable Analytical Method for Solving Higher-Order Initial Value Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.
    7. Dubey, Ved Prakash & Dubey, Sarvesh & Kumar, Devendra & Singh, Jagdev, 2021. "A computational study of fractional model of atmospheric dynamics of carbon dioxide gas," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. El-Ajou, Ahmad & Abu Arqub, Omar & Momani, Shaher & Baleanu, Dumitru & Alsaedi, Ahmed, 2015. "A novel expansion iterative method for solving linear partial differential equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 119-133.
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