IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p1961-d833185.html
   My bibliography  Save this article

An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

Author

Listed:
  • Mamta Kapoor

    (Department of Mathematics, Lovely Professional University, Phagwara 144411, Punjab, India
    These authors contributed equally to this work and are co-first authors.)

  • Nehad Ali Shah

    (Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
    These authors contributed equally to this work and are co-first authors.)

  • Salman Saleem

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Wajaree Weera

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

Abstract

In the present research paper, an iterative approach named the iterative Shehu transform method is implemented to solve time-fractional hyperbolic telegraph equations in one, two, and three dimensions, respectively. These equations are the prominent ones in the field of physics and in some other significant problems. The efficacy and authenticity of the proposed method are tested using a comparison of approximated and exact results in graphical form. Both 2D and 3D plots are provided to affirm the compatibility of approximated-exact results. The iterative Shehu transform method is a reliable and efficient tool to provide approximated and exact results to a vast class of ODEs, PDEs, and fractional PDEs in a simplified way, without any discretization or linearization, and is free of errors. A convergence analysis is also provided in this research.

Suggested Citation

  • Mamta Kapoor & Nehad Ali Shah & Salman Saleem & Wajaree Weera, 2022. "An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1961-:d:833185
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/1961/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/12/1961/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Seyma Tuluce Demiray & Hasan Bulut & Fethi Bin Muhammad Belgacem, 2015. "Sumudu Transform Method for Analytical Solutions of Fractional Type Ordinary Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-6, June.
    2. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    3. Prakash, Amit & Kumar, Manoj & Sharma, Kapil K., 2015. "Numerical method for solving fractional coupled Burgers equations," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 314-320.
    4. Hasan Bulut & Haci Mehmet Baskonus & Fethi Bin Muhammad Belgacem, 2013. "The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, September.
    5. Khan, Mair & Salahuddin, T. & Malik, M.Y. & Alqarni, M.S. & Alqahtani, A.M., 2020. "Numerical modeling and analysis of bioconvection on MHD flow due to an upper paraboloid surface of revolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    6. Ali, Usman & Malik, M.Y. & Rehman, Khalil Ur & Alqarni, M.S., 2020. "Exploration of cubic autocatalysis and thermal relaxation in a non-Newtonian flow field with MHD effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    7. Wenfeng He & Nana Chen & Ioannis Dassios & Nehad Ali Shah & Jae Dong Chung, 2021. "Fractional System of Korteweg-De Vries Equations via Elzaki Transform," Mathematics, MDPI, vol. 9(6), pages 1-18, March.
    8. Shailesh A. Bhanotar & Mohammed K. A. Kaabar, 2021. "Analytical Solutions for the Nonlinear Partial Differential Equations Using the Conformable Triple Laplace Transform Decomposition Method," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-18, August.
    9. 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.
    10. Adem Kiliçman & Hassan Eltayeb & Ravi P. Agarwal, 2010. "On Sumudu Transform and System of Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-11, April.
    11. Hwajoon Kim, 2017. "The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, June.
    12. Shehu Maitama, 2016. "A Hybrid Natural Transform Homotopy Perturbation Method for Solving Fractional Partial Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2016, pages 1-7, September.
    13. Suleyman Cetinkaya & Ali Demir & Hulya Kodal Sevindir, 2021. "Solution of Space-Time-Fractional Problem by Shehu Variational Iteration Method," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-8, April.
    14. M. Higazy & Sudhanshu Aggarwal & Taher A. Nofal & Hijaz Ahmad, 2020. "Sawi Decomposition Method for Volterra Integral Equation with Application," Journal of Mathematics, Hindawi, vol. 2020, pages 1-13, December.
    15. Abbas, Nadeem & Malik, M.Y. & Alqarni, M.S. & Nadeem, S., 2020. "Study of three dimensional stagnation point flow of hybrid nanofluid over an isotropic slip surface," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akgül, Esra Karatas & Akgül, Ali & Yavuz, Mehmet, 2021. "New Illustrative Applications of Integral Transforms to Financial Models with Different Fractional Derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    4. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    5. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    6. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    7. 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.
    8. Shumaila Naz & Attia Rani & Muhammad Shakeel & Nehad Ali Shah & Jae Dong Chung, 2022. "Novel Soliton Solutions of the Fractional Riemann Wave Equation via a Mathematical Method," Mathematics, MDPI, vol. 10(22), pages 1-21, November.
    9. Owolabi, Kolade M., 2018. "Numerical patterns in reaction–diffusion system with the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 160-169.
    10. Eslami, Mostafa, 2016. "Exact traveling wave solutions to the fractional coupled nonlinear Schrodinger equations," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 141-148.
    11. Attia Rani & Muhammad Shakeel & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Prem Junsawang, 2022. "Application of the Exp − φ ξ -Expansion Method to Find the Soliton Solutions in Biomembranes and Nerves," Mathematics, MDPI, vol. 10(18), pages 1-12, September.
    12. Biswas, Nirmalendu & Mandal, Dipak Kumar & Manna, Nirmal K. & Benim, Ali Cemal, 2023. "Enhanced energy and mass transport dynamics in a thermo-magneto-bioconvective porous system containing oxytactic bacteria and nanoparticles: cleaner energy application," Energy, Elsevier, vol. 263(PB).
    13. Muhammad Shakeel & Attaullah & Mohammed Kbiri Alaoui & Ahmed M. Zidan & Nehad Ali Shah & Wajaree Weera, 2022. "Closed-Form Solutions in a Magneto-Electro-Elastic Circular Rod via Generalized Exp-Function Method," Mathematics, MDPI, vol. 10(18), pages 1-21, September.
    14. Nazir, Aqsa & Ahmed, Naveed & Khan, Umar & Mohyud-din, Syed Tauseef, 2020. "On stability of improved conformable model for studying the dynamics of a malnutrition community," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    15. Abdeljawad, Thabet & Atangana, Abdon & Gómez-Aguilar, J.F. & Jarad, Fahd, 2019. "On a more general fractional integration by parts formulae and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    16. Gómez-Aguilar, J.F., 2020. "Chaos and multiple attractors in a fractal–fractional Shinriki’s oscillator model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    17. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    18. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    19. Ismail, G.M. & Abdl-Rahim, H.R. & Abdel-Aty, A. & Kharabsheh, R. & Alharbi, W. & Abdel-Aty, M., 2020. "An analytical solution for fractional oscillator in a resisting medium," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    20. Pundikala Veeresha & Doddabhadrappla Gowda Prakasha & Dumitru Baleanu, 2019. "An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation," Mathematics, MDPI, vol. 7(3), pages 1-18, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1961-:d:833185. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.