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Modified Modelling for Heat Like Equations within Caputo Operator

Author

Listed:
  • Hassan Khan

    (Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan)

  • Adnan Khan

    (Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan)

  • Maysaa Al-Qurashi

    (Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia)

  • Rasool Shah

    (Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan)

  • Dumitru Baleanu

    (Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
    Institute of Space Sciences, 077125 Magurele-Bucharest, Romania)

Abstract

The present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the Iterative Laplace transform method. The proposed method provides the series form solution that has the desired rate of convergence towards the exact solution of the problems. It is observed that the suggested method provides closed-form solutions. The reliability of the method is confirmed with the help of some illustrative examples. The graphical representation has been made for both fractional and integer-order solutions. Numerical solutions that are in close contact with the exact solutions to the problems are investigated. Moreover, the sample implementation of the present method supports the importance of the method to solve other fractional-order problems in sciences and engineering.

Suggested Citation

  • Hassan Khan & Adnan Khan & Maysaa Al-Qurashi & Rasool Shah & Dumitru Baleanu, 2020. "Modified Modelling for Heat Like Equations within Caputo Operator," Energies, MDPI, vol. 13(8), pages 1-14, April.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:8:p:2002-:d:347078
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    References listed on IDEAS

    as
    1. Limei Yan, 2013. "Numerical Solutions of Fractional Fokker-Planck Equations Using Iterative Laplace Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, December.
    2. Bo Fu & Chenxi Ouyang & Chaoshun Li & Jinwen Wang & Eid Gul, 2019. "An Improved Mixed Integer Linear Programming Approach Based on Symmetry Diminishing for Unit Commitment of Hybrid Power System," Energies, MDPI, vol. 12(5), pages 1-14, March.
    3. Hong Gao & Chao Liu & Chao He & Xiaoxiao Xu & Shuangying Wu & Yourong Li, 2012. "Performance Analysis and Working Fluid Selection of a Supercritical Organic Rankine Cycle for Low Grade Waste Heat Recovery," Energies, MDPI, vol. 5(9), pages 1-15, August.
    4. Delia D’Agostino & Paolo Zangheri & Luca Castellazzi, 2017. "Towards Nearly Zero Energy Buildings in Europe: A Focus on Retrofit in Non-Residential Buildings," Energies, MDPI, vol. 10(1), pages 1-15, January.
    5. Yulia Glavatskaya & Pierre Podevin & Vincent Lemort & Osoko Shonda & Georges Descombes, 2012. "Reciprocating Expander for an Exhaust Heat Recovery Rankine Cycle for a Passenger Car Application," Energies, MDPI, vol. 5(6), pages 1-15, June.
    6. Robin Bornoff, 2019. "Extraction of Boundary Condition Independent Dynamic Compact Thermal Models of LEDs—A Delphi4LED Methodology," Energies, MDPI, vol. 12(9), pages 1-10, April.
    7. Ping-Huan Kuo & Chiou-Jye Huang, 2018. "A High Precision Artificial Neural Networks Model for Short-Term Energy Load Forecasting," Energies, MDPI, vol. 11(1), pages 1-13, January.
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    Cited by:

    1. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    2. Faridul Islam & Aviral Kumar Tiwari & Wing-Keung Wong, 2021. "Editorial and Ideas for Research Using Mathematical and Statistical Models for Energy with Applications," Energies, MDPI, vol. 14(22), pages 1-4, November.
    3. Mohammed Kbiri Alaoui & Kamsing Nonlaopon & Ahmed M. Zidan & Adnan Khan & Rasool Shah, 2022. "Analytical Investigation of Fractional-Order Cahn–Hilliard and Gardner Equations Using Two Novel Techniques," Mathematics, MDPI, vol. 10(10), pages 1-19, May.

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