Double Mohand Integral Transform for Solving Wave Equations

Authors

  • Muhammad Abbas Department of Physics, Government Post Graduate College Karak, Khyber Pakhtunkhwa, Pakistan
  • Shahab Ali Department of Physics, Government Post Graduate College Karak, Khyber Pakhtunkhwa, Pakistan
  • Shakir Ullah Department of Physics, Government Post Graduate College Karak, Khyber Pakhtunkhwa, Pakistan
  • Wahid Rehman Department of Mathematics, Universidade Federal do Rio Grande do Sul Campus Do Vale, Brazil.

DOI:

https://doi.org/10.48165/gjs.2025.2109

Keywords:

Double Mohand, transform method, Wave equation, partial differential, equations

Abstract

Many fields of the physical sciences like physics, chemistry and mathematics use partial  differential equations to model a physical system. As a result, there are diverse techniques  in the literature for the solution of partial differential equations which tries to attain  symmetry. This paper proposes a fresh double transform method recognized as the double  Mohand Transform Method. Besides the explanation and major remarks of the proposed  double transform method, new results on partial derivatives are also given. Moreover, to  validate the importance of the double Mohand Transform Method in solving systems of  partial differential equations, a variety of symmetric examples on the wave equation with  various properties are solved using this approach.

References

[1] Debnath, L., & Bhatta, D. (n.d.). Integral transforms and their applications (2nd ed.). Chapman & Hall/CRC.

[2] Raisinghania, M. D. (n.d.). Advanced differential equations. S Chand & Co. Ltd.

[3] Jeffrey, A. (n.d.). Advanced engineering mathematics. Harcourt Academic Press.

[4] Stroud, K. A., & Booth, D. J. (n.d.). Engineering mathematics. Industrial Press Inc.

[5] Abouelregal, A. E., Ahmad, H., & Yao, S. W. (2020). Functionally graded piezoelectric medium exposed to a movable heat flow based on a heat equation with a memory-dependent derivative. Materials, 13(18), 3953.

[6] Aggarwal, S., & Sharma, S. D. (2019). Sumudu transform of error function. Journal of Applied Science and Computations, 6, 1222–1231.

[7] Elzaki, T. M. (2011). The new integral transform Elzaki Transform. Global Journal of Pure and Applied Mathematics, 7, 57–64.

[8] Hassan, M. A., & Elzaki, T. M. (2020). Double Elzaki transform decomposition method for solving non-linear partial differential equations. Journal of Applied Mathematics and Physics, 8, 1463–1471.

[9] Ahmed, S., & Elzaki, T. M. (2020). On the comparative study integro-differential equations using difference numerical methods. Journal of King Saud University – Science, 32, 84–89.

[10] Aggarwal, S., Chauhan, R., & Sharma, N. (2018). Application of Elzaki transform for solving linear Volterra integral equations of first kind. International Journal of Research in Advent Technology, 6, 3687–3692.

[11] Ahmad, H., & Khan, T. A. (2020). Variational iteration algorithm I with an auxiliary parameter for the solution of differential equations of motion for simple and damped mass–spring systems. Noise & Vibration Worldwide, 51(1–2), 12–20.

[12] Wang, F., Ahmad, I., Ahmad, H., Alsulami, M. D., Alimgeer, K. S., Cesarano, C., & Nofal, T. A. (2021). Meshless method based on RBFs for solving three-dimensional multi-term time fractional PDEs arising in engineering phenomenons. Journal of King Saud University – Science, 33(8), 101604.

[13] Ojo, G. O., & Mahmudov, N. I. (2021). Aboodh Transform iterative method for spatial diffusion of a biological population with fractional-order. Mathematics, 9, 155.

[14] Aggarwal, S., Sharma, N., & Chauhan, R. (2018). Application of Aboodh transform for solving linear Volterra integrodifferential equations of second kind. International Journal of Research in Advent Technology, 7, 156–158.

[15] Kashuri, A., & Fundo, A. (2013). A new integral transform. Advances in Theoretical and Applied Mathematics, 8, 27–43.

[16] Mohand, M., & Mahgoub, A. (2017). The new integral transform Mohand Transform. Advances in Theoretical and Applied Mathematics, 12, 113–120.

[17] Patra, A., Baliarsingh, P., & Dutta, H. (2022). Solution to fractional evolution equation using Mohand transform. Mathematics and Computers in Simulation, 200, 557–570.

[18] Khandelwal, R., & Khandelwal, Y. (2020). Solution of Blasius equation concerning with Mohand transform. International Journal of Applied and Computational Mathematics, 6, 128.

[19] Aggarwal, S., & Chaudhary, R. (2019). A comparative study of Mohand and Laplace transforms. Journal of Emerging Technologies and Innovative Research, 6, 230–240.

[20] Kamal, A., & Sedeeg, H. (2016). The new integral transform Kamal Transform. Advances in Theoretical and Applied Mathematics, 11, 451–458.

[21] Aruldass, A. R., Pachaiyappan, D., & Park, C. (2021). Kamal transform and ULAM stability of differential equations. Journal of Applied Analysis and Computation, 11, 1631–1639.

[22] Samar, C. P., & Saxena, H. (2021). Solution of generalized fractional kinetic equation by Laplace and Kamal transformation. International Journal of Mathematics Trends and Technology, 67, 38–43.

[23] Aggarwal, S., Chauhan, R., & Sharma, N. (2018). A new application of Kamal transform for solving linear Volterra integral equations. International Journal of Latest Technology in Engineering, Management & Applied Science, 6, 2081–2088.

[24] Kilicman, A., & Gadain, H. E. (2009). An application of double Laplace transforms and Sumudu transform. Lobachevskii Journal of Mathematics, 30, 214–223.

[25] Jadhav, S., Basotia, V., & Hiwarekar, A. (2022). An application of double Elzaki transform in partial differential equations. International Journal of Advanced Research in Science, Communication and Technology, 2(1), 181–186.

[26] Aboodh, K. S., Farah, R. A., Almardy, I. A., & Almostafa, F. A. (2017). Solution of telegraph equation by using double Aboodh transform. Elixir Applied Mathematics, 110, 48213–48217.

[27] Patil, D. P. (2021). Solution of wave equation by double Laplace and double Sumudu transform. VidyaBharati International Interdisciplinary Research Journal, Sp. Iss., 135–138.

[28] Eltayeb, H., & Kiliçman, A. A. (2013). A note on double Laplace transform and telegraphic equations. Abstract and Applied Analysis, 2013, 932578.

[29] Alfaqeih, S., & Misirli, E. (2020). On double Shehu transform and its properties with applications. International Journal of Analysis and Applications, 18, 381–395.

[30] Sonawane, S. M., & Kiwne, S. B. (2019). Double Kamal transforms: Properties and Applications. Journal of Applied Science and Computations, 4, 1727–1739.

[31] Ganie, J. A., Ahmad, A., & Jain, R. (2018). Basic analogue of double Sumudu transform and its applicability in population dynamics. Asian Journal of Mathematics and Statistics, 11, 12–17.

[32] Eltayeb, H., & Kiliçman, A. (2010). On double Sumudu transform and double Laplace transform. Malaysian Journal of Mathematical Sciences, 4, 17–30.

[33] Tchuenche, J. M., & Mbare, N. S. (2007). An application of the double Sumudu transform. Applied Mathematical Sciences, 1, 31–39.

[34] Al-Omari, S. K. Q. (2012). Generalized functions for double Sumudu transformation. International Journal of Algebra, 6, 139–146.

[35] Eshag, M. O. (2017). On double Laplace transform and double Sumudu transform. American Journal of Engineering Research, 6, 312–317.

[36] Ahmed, Z., Idrees, M. I., Belgacem, F. B. M., & Perveen, Z. (2020). On the convergence of double Sumudu transform. Journal of Nonlinear Sciences and Applications, 13, 154–162.

[37] Idrees, M. I., Ahmed, Z., Awais, M., & Perveen, Z. (2018). On the convergence of double Elzaki transform. International Journal of Advanced and Applied Sciences, 5, 19–24.

[38] Ahmed, S., Elzaki, T., Elbadri, M., & Mohamed, M. Z. (2021). Solution of partial differential equations by new double integral transform (Laplace–Sumudu transform). Ain Shams Engineering Journal, 12, 4045–4049.

[39] Saadeh, R., Qazza, A., & Burqan, A. (2022). On the Double ARA-Sumudu transform and its applications. Mathematics, 10, 2581.

[40] Qazza, A., Burqan, A., Saadeh, R., & Khalil, R. (2022). Applications on Double ARA–Sumudu Transform in Solving Fractional Partial Differential Equations. Symmetry, 14, 1817.

[41] Meddahi, M., Jafari, H., & Yang, X. J. (2021). Towards new general double integral transform and its applications to differential equations. Mathematical Methods in the Applied Sciences, 45, 1916–1933.

[42] Ullah, S., & Aggarwal, S. (2024). Properties and Application of Double Mohand Transform. Journal of Advanced Research in Applied Mathematics and Statistics, 9(3&4), 1–12.

[43] Bulut, H., Baskonus, H. M., & Tuluce, S. (2012). The Solution of Wave Equations by Sumudu Transform Method. Journal of Advanced Research in Applied Mathematics, 4, 66–72.

[44] Sedeeg, A. K., Mahamoud, Z. I., & Saadeh, R. (2022). Using Double Integral Transform (Laplace–ARA Transform) in Solving Partial Differential Equations. Symmetry, 14, 2418.

Published

2025-08-23

How to Cite

Double Mohand Integral Transform for Solving Wave Equations. (2025). Global Journal of Sciences, 2(1), 99-111. https://doi.org/10.48165/gjs.2025.2109