Mathematics and Computational Sciences

A New Integral Transform for Solving Integral and Ordinary Differential Equations

Document Type : Original Article

Authors

Mohammed Taimah Yasser 1, 2
Hassan Kamil Jassim 3

1 Department of mathematics, Faculty of pure Sciences, University of Thi Qar, Naseryah, Iraq.

2 College of Technical Engineering, National University of Science and Technology, Thi-Qar, Iraq.

3 Department of mathematics, Faculty of pure Sciences, University of Thi Qar, Naseryah, Iraq

https://doi.org/10.30511/mcs.2025.2045547.1254
Abstract
In this research paper, we introduce a new transform belonging to the class of Laplace transforms, called the Yasser-Jassim Transform (YJ Transform). We explore its properties and compare it to the classical Laplace transform. Furthermore, we provide proofs for the key properties associated with this transform and demonstrate its application in solving differential and integral equations. By employing this new transform, we can reduce the original problem to an algebraic equation that can be solved directly, followed by applying the inverse transform to obtain the solution to the original problem.

Keywords

Integral Transform
linear Differential Equation
Integral Equation
Voltera Equation
Voltera-Integro Equation

Subjects

[1] Abdelrahim Mahgoub, M. M. (2017). The new integral transform Mohand transform. Advances in Theoretical and Applied Mathematics, 12(2), 113120. 1
[2] Abdelrahim Mahgoub, M. M. (2019). The new integral transform Sawi transform. Advances in Theoretical and Applied Mathematics, 14(1), 8187. 1
[3] Aboodh, K. S. (2013). The new integral transform Aboodh transform. Global Journal of Pure and Applied Mathematics, 9(1), 3543. 1
[4] Ahmad, H., & Jassim, H. K. (2024). An analytical technique to obtain approximate solutions of nonlinear fractional PDEs. Journal of Education for Pure Science-University of Thi-Qar, 14(1), 107116. 1
[5] Ali, U., Malik, M. Y., Rehman, K. U., & 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, 549, 124349. 1
[6] Bokhari, A., Baleanu, D., & Belgacem, R. (2020). Application of Shehu transform to Atangana-Baleanu derivatives. Journal of Mathematics and Computer Science, 20(2), 101107. 1
[7] Bölükbas, D., & Ergin, A. A. (2005). A Radon transform interpretation of the physical optics integral. Microwave and Optical Technology Letters, 44(3), 5972. 1
[8] Davies, B. (2002). Integral transforms and their applications. Springer. 1
[9] Eltayeb, H., Kiliman, A., & Fisher, B. (2010). A new integral transform and associated distributions. Integral Transforms and Special Functions, 21(5), 367379. 1
[10] Elzaki, T. M. (2011). The new integral transform Elzaki transform. Global Journal of Pure and Applied Mathematics, 7(1), 5764. 1
[11] Elzaki, T. M., Elzaki, S. M., & Hilal, E. M. A. (2012). Elzaki and Sumudu transforms for solving some differential equations. Global Journal of Pure and Applied Mathematics, 8(2), 167173. 1
[12] Higgins, W. E., & Munson, D. C. (1988). A Hankel transform approach to tomographic image reconstruction. IEEE Transactions on Medical Imaging, 7, 5972. 1
[13] Hussein, M. A. (2022). Approximate methods for solving fractional differential equations. Journal of Education for Pure Science-University of Thi-Qar, 12(2), 3240. 1
[14] Hussein, G. A., & Ziane, D. (2024). A new approximation solutions for fractional order biological population model. Journal of Education for Pure Science-University of Thi-Qar, 10(3), 120. 1
[15] Hussein, E. A., Mohammed, M. G., & Hussein, A. J. (2021). Solution of the second and fourth order differential
equations using irbfn method. Journal of Education for Pure Science-University of Thi-Qar, 11(2), 117. 1
[16] Issa, S. A., & Tajadodi, H. (2024a). Solve of fractional telegraph equation via Yang decomposition method. Journal
of Education for Pure Science-University of Thi-Qar, 14(4), 96113. 1
[17] Issa, S. A., & Tajadodi, H. (2024b). Yang Adomian decomposition method for solving PDEs. Journal of Education
for Pure Science-University of Thi-Qar, 14(2), 1425. 1, 3
[18] Jafari, H., Jassim, H. K., & Baleanu, D. (2016). On the existence and uniqueness of solutions for local fractional differential equations. Entropy, 18(1), 19. https://doi.org/10.3390/e18010001 1
[19] Jassim, H. K., Salman, A. T., Ahmed, H., Hassan, N. J., & Hashoosh, A. E. (2023). Solving nonlinear fractional PDEs by Elzaki homotopy perturbation method. In AIP Conference Proceedings.Vol. 2834, p. 080101). AIP Publishing.1
[20] Jassim, H. K., & Mohammed, M. G. (2021). Natural homotopy perturbation method for solving nonlinear fractional gas dynamics equations. International Journal of Nonlinear Analysis and Applications, 12(1), 813821. 1
[21] Jawad, Z. R., & Al-Jaberi, A. K. (2024). A modified of fourth-order partial differential equations model based on isophote direction to noise image removal. Journal of Education for Pure Science-University of Thi-Qar, 10(3),115. 1
[22] Kamal, H., & Sedeeg, A. (2016). The new integral transform Kamal transform. Advances in Theoretical and Applied Mathematics, 11(4), 451458. 1
[23] Martinez, F., Mohammed, P. O., & Valdés, J. N. (2022). Non-conformable fractional Laplace transform. Kragujevac Journal of Mathematics, 46(3), 341354. 2.3
[24] Matar, Z. S., Abdul Kadeem, S. R., & Naser, A. H. (2024). A new approach to video summary generation. Journal of Education for Pure Science-University of Thi-Qar, 10(3), 120. 1
[25] Sedeeg, A. K. H., Abdelrahim Mahgoub, M. M., & SaifSaeed, M. A. (2016). An application of the new integral Aboodh transform in cryptography. Pure and Applied Mathematics Journal, 5(5), 151154. 1
[26] Vivas-Cortez, M., Valdés, J. N., Hernández, J. E. H., Velasco, J. V., & Larreal, O. (2021). On non-conformable fractional Laplace transform. Applied Mathematics & Information Sciences, 15(4), 403409. 2.4
[27] Vivas-Cortez, M. J. (2021). On the generalized Laplace transform. 2.5
[28] Zair, M. Y., & Cherif, M. H. (2024). The numerical solutions of 3-dimensional fractional differential equations. Journal of Education for Pure Science-University of Thi-Qar, 14(2), 113. 1
Mathematics and Computational Sciences
Volume 6, Issue 2
Spring 2025
Pages 32-42

  • Receive Date 11 November 2024
  • Revise Date 24 February 2025
  • Accept Date 24 February 2025

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