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Comparison of the results obtained by Iman transform with Laplace transform

Year 2024, Volume: 8 Issue: 2, 233 - 242

Nihal Özdoğan

https://doi.org/10.38088/jise.1497589

Abstract

Many processes in the real world are characterised by principles which are defined in the form of expressions involving rates of change. Mathematically, rates are derivatives and expressions are equations so we have differential equations. Differential equations play an important role for modelling many problems in different scientific fields. Sometimes, the calculations to solve these equations can be very complex and ultimately frustrating. For this reason, many integral transform methods were proposed by researchers. However, integral transform methods can give consistent solutions to many complex problems and have many application areas such as physics, mechanics, engineering, astronomy. In this work, two integral transforms, Iman transform and the well-known Laplace transform were studied comparatively to facilitate the solution of linear ordinary differential equations with constant coefficients. Applications of these two transforms show that these integral transform methods are closely related to each other.

Keywords

Iman Transform Laplace Transform Integral Transform Differential Equations.

References

  • [1] Aggarwal, S. and Gupta, A.R. (2019). Dualities between Mohand Transform and Some Useful Integral Transforms. International Journal of Recent Tecnology and Engineering, 8(3): 843-847.
  • [2] Sornkaew, P. and Phollamat, K. (2021). Solution of Partial Differential Equations by Using Mohand Transforms. Journal of Physics: Conference Series, Vol. 1850, Iss. 1.
  • [3] Saadeh, R., Qazza, A. and Burqan, A. (2020). A New Integral Transform: Ara Transform and Its Properties and Applications. Symmetry, 12 (6), 925.
  • [4] Kushare, S.R., Patil, D.P. and Takate, A.M. (2021). The New Integral Transform “KUSHARE Transform”. International Journal of Advances in Engineering and Management, 3 (9): 1589-1592.
  • [5] Johansyah, M.D., Supriatna, A.K., Rusyaman E. and Saputra, J. (2021). Solving Differential Equations of Fractional Order Using Combined Adomian Decomposition Method with Kamal Integral Transformation. Mathematics and Statistics, 10 (1): 187-194.
  • [6] Patil, D.P. (2021). Aboodh and Mahgoub Transform in Boundary Value Problems of Ordinary Differential Equations. International Journal of Advanced Research in Science, Communication and Technology, 6 (1): 67-75.
  • [7] Turab, A., Hilmi, H., Guirao, J.L.G., Jalil, S., Chorfi, N. and Mohammed, P.O. (2024). The Rishi Transform Method for solving multi-high order fractional differential equations with constant coefficients, AIMS Mathematics, 9 (2): 3798-3809.
  • [8] Kuffi, E. and Maktoof, S.F. (2021). “Emad-Falih Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24 (8): 2381-2390.
  • [9] Gupta, R. (2020). On Novel Integral Transform: Rohit Transform and Its Application to Boundary Value Problems. ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences, 4 (1): 08-12.
  • [10] Katre, N.T. and Katre, R.T. (2021). A comparative study of Laplace and Kamal transforms. International Conference on Research Frontiers in Sciences (ICRFS), Nagpur, India.
  • [11]Rashdi, H.Z. (2022). Using Anuj Transform to Solve Ordinary Differential Equations with Variable Coefficients. Scientific Journal for the Faculty of Scientific-Sirte University, 2 (1): 38-42.
  • [12] Patil, D.P., Tile, G.K. and Shinde, P.D. (2022). Volterra Integral Equations of First Kind by Using Anuj Transform. International Journal of Advances in Engineering and Management, 4 (5): 917-920.
  • [13] Ongun, M.Y. (2011). The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4^+T cells. Mathematical and Computer Modelling, 53 (5): 597-603.
  • [14] Laplace, P.S. (1820). Th´eorie Analytique des Probabiliti´es. Vol. I, Part 2, Lerch, Paris.
  • [15] Sanap, R.S. and Patil, D.P. (2022). Kushare Integral Transform for Newton’s Law of Cooling. International Journal of Advances in Engineering and Management, 4 (1): 166-170.
  • [16] Patil, D.P., Malpani, S.K. and Shinde, P.N. (2022). Convolution Theorem for Kushare Transform and Applications in Convolution Type Volterra Integral Equations of First Kind. International Journal of Scientific Development and Research, 7 (7): 262-267.
  • [17] Patil, D.P., Borse, S. and Kapadi, D. (2022). Applications of Emad Falih Transform for General Solution of Telegraph Equation. International Journal of Advanced Research in Science, Engineering and Technology, 9 (6): 19450-19454.
  • [18] Fadhil, R.A. and Alkfari, B.H.A. (2023). Convolution HY Transform for second kind of linear Volterra integral equation, Al-Kadhum 2nd International Conference on Modern Applications of Information and Communication Technology, Baghdad, Iraq, 8-9 December.
  • [19] Ahmadi, S.A.P., Hosseinzadeh, H. And Cherati, A.Z. (2019). A New Integral Transform for Solving Higher Order Linear Ordinary Laquerre and Hermite Differential Equations. International Journal of Applied and Computational Mathematics, 5 (142): 1-7.
  • [20] Maitama, S. and Zhao, W. (2019). New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations. International Journal of Analysis and Applications, 17 (2): 1-22.
  • [21] Maktoof, S.F., Kuffi, E. and Abbas, E.S. (2021). “Emad-Sara Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24 (7): 1985-1994.
  • [22] Khan, Z.H. and Khan, W.A. (2008). N-Transform-Properties and Applications. NUST Journal of Engineering Sciences, 1 (1): 127-133.
  • [23] Elzaki, T.M. (2011). The New Integral Transform “Elzaki Transform”. Global Journal of Pure and Applied Mathematics, 7 (1): 57-64.
  • [24] Srivastava, H.M., Luo, M. and Raina, R.K. (2015). A New Integral Transform and Its Applications. Acta Mathematica Scientia, 35 (6): 1386-1400.
  • [25] Yang, X-J. (2016). A New Integral Transform Method for Solving Steady Heat-Transfer Problem. Thermal Science, 20 (3): 639-642.
  • [26] Mushtt, I.Z. and Kuffi, E.A. (2023). Sadik and Complex Sadik Integral Transforms of System of Ordinary Differential Equations. Iraqi Journal for Computer Science and Mathematics, 4 (1), 181-190.
  • [27] Oyewumi, A.A. and Oderinu, R.A. (2022). Application of the Combined Aboodh and Reduced Differential Transform Methods to the Fisher’s Type Equations. Asian Journal of Pure and Applied Mathematics, 4 (1): 572-585.
  • [28] Kılıcman, A. and Gadain, H.E. (2010). On the applications of Laplace and Sumudu Transforms. Journal of The Franklin Institute, 347 (5): 848-862.
  • [29] Elzaki, T.M. and Ezaki, S.M. (2011). On the connections between Laplace and ELzaki transforms. Advances in Theoretical and Applied Mathematics, 6 (1): 1-10.
  • [30] Almardy, I.A. (2023). The New Integral Transform “Iman Transform”. International Journal of Advanced Research in Science, Communication and Technology, 3 (1): 1-5.
  • [31] Almardy, I.A., Farah, R.A. and Elkeer, M.A. (2023). On the Iman Transform and Systems of Ordinary Differential Equations. International Journal of Advanced Research in Science, Communication and Technology, 3 (1): 577-580.

Year 2024, Volume: 8 Issue: 2, 233 - 242

Nihal Özdoğan

https://doi.org/10.38088/jise.1497589

Abstract

References

  • [1] Aggarwal, S. and Gupta, A.R. (2019). Dualities between Mohand Transform and Some Useful Integral Transforms. International Journal of Recent Tecnology and Engineering, 8(3): 843-847.
  • [2] Sornkaew, P. and Phollamat, K. (2021). Solution of Partial Differential Equations by Using Mohand Transforms. Journal of Physics: Conference Series, Vol. 1850, Iss. 1.
  • [3] Saadeh, R., Qazza, A. and Burqan, A. (2020). A New Integral Transform: Ara Transform and Its Properties and Applications. Symmetry, 12 (6), 925.
  • [4] Kushare, S.R., Patil, D.P. and Takate, A.M. (2021). The New Integral Transform “KUSHARE Transform”. International Journal of Advances in Engineering and Management, 3 (9): 1589-1592.
  • [5] Johansyah, M.D., Supriatna, A.K., Rusyaman E. and Saputra, J. (2021). Solving Differential Equations of Fractional Order Using Combined Adomian Decomposition Method with Kamal Integral Transformation. Mathematics and Statistics, 10 (1): 187-194.
  • [6] Patil, D.P. (2021). Aboodh and Mahgoub Transform in Boundary Value Problems of Ordinary Differential Equations. International Journal of Advanced Research in Science, Communication and Technology, 6 (1): 67-75.
  • [7] Turab, A., Hilmi, H., Guirao, J.L.G., Jalil, S., Chorfi, N. and Mohammed, P.O. (2024). The Rishi Transform Method for solving multi-high order fractional differential equations with constant coefficients, AIMS Mathematics, 9 (2): 3798-3809.
  • [8] Kuffi, E. and Maktoof, S.F. (2021). “Emad-Falih Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24 (8): 2381-2390.
  • [9] Gupta, R. (2020). On Novel Integral Transform: Rohit Transform and Its Application to Boundary Value Problems. ASIO Journal of Chemistry, Physics, Mathematics and Applied Sciences, 4 (1): 08-12.
  • [10] Katre, N.T. and Katre, R.T. (2021). A comparative study of Laplace and Kamal transforms. International Conference on Research Frontiers in Sciences (ICRFS), Nagpur, India.
  • [11]Rashdi, H.Z. (2022). Using Anuj Transform to Solve Ordinary Differential Equations with Variable Coefficients. Scientific Journal for the Faculty of Scientific-Sirte University, 2 (1): 38-42.
  • [12] Patil, D.P., Tile, G.K. and Shinde, P.D. (2022). Volterra Integral Equations of First Kind by Using Anuj Transform. International Journal of Advances in Engineering and Management, 4 (5): 917-920.
  • [13] Ongun, M.Y. (2011). The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4^+T cells. Mathematical and Computer Modelling, 53 (5): 597-603.
  • [14] Laplace, P.S. (1820). Th´eorie Analytique des Probabiliti´es. Vol. I, Part 2, Lerch, Paris.
  • [15] Sanap, R.S. and Patil, D.P. (2022). Kushare Integral Transform for Newton’s Law of Cooling. International Journal of Advances in Engineering and Management, 4 (1): 166-170.
  • [16] Patil, D.P., Malpani, S.K. and Shinde, P.N. (2022). Convolution Theorem for Kushare Transform and Applications in Convolution Type Volterra Integral Equations of First Kind. International Journal of Scientific Development and Research, 7 (7): 262-267.
  • [17] Patil, D.P., Borse, S. and Kapadi, D. (2022). Applications of Emad Falih Transform for General Solution of Telegraph Equation. International Journal of Advanced Research in Science, Engineering and Technology, 9 (6): 19450-19454.
  • [18] Fadhil, R.A. and Alkfari, B.H.A. (2023). Convolution HY Transform for second kind of linear Volterra integral equation, Al-Kadhum 2nd International Conference on Modern Applications of Information and Communication Technology, Baghdad, Iraq, 8-9 December.
  • [19] Ahmadi, S.A.P., Hosseinzadeh, H. And Cherati, A.Z. (2019). A New Integral Transform for Solving Higher Order Linear Ordinary Laquerre and Hermite Differential Equations. International Journal of Applied and Computational Mathematics, 5 (142): 1-7.
  • [20] Maitama, S. and Zhao, W. (2019). New Integral Transform: Shehu Transform a Generalization of Sumudu and Laplace Transform for Solving Differential Equations. International Journal of Analysis and Applications, 17 (2): 1-22.
  • [21] Maktoof, S.F., Kuffi, E. and Abbas, E.S. (2021). “Emad-Sara Transform” a new integral transform. Journal of Interdisciplinary Mathematics, 24 (7): 1985-1994.
  • [22] Khan, Z.H. and Khan, W.A. (2008). N-Transform-Properties and Applications. NUST Journal of Engineering Sciences, 1 (1): 127-133.
  • [23] Elzaki, T.M. (2011). The New Integral Transform “Elzaki Transform”. Global Journal of Pure and Applied Mathematics, 7 (1): 57-64.
  • [24] Srivastava, H.M., Luo, M. and Raina, R.K. (2015). A New Integral Transform and Its Applications. Acta Mathematica Scientia, 35 (6): 1386-1400.
  • [25] Yang, X-J. (2016). A New Integral Transform Method for Solving Steady Heat-Transfer Problem. Thermal Science, 20 (3): 639-642.
  • [26] Mushtt, I.Z. and Kuffi, E.A. (2023). Sadik and Complex Sadik Integral Transforms of System of Ordinary Differential Equations. Iraqi Journal for Computer Science and Mathematics, 4 (1), 181-190.
  • [27] Oyewumi, A.A. and Oderinu, R.A. (2022). Application of the Combined Aboodh and Reduced Differential Transform Methods to the Fisher’s Type Equations. Asian Journal of Pure and Applied Mathematics, 4 (1): 572-585.
  • [28] Kılıcman, A. and Gadain, H.E. (2010). On the applications of Laplace and Sumudu Transforms. Journal of The Franklin Institute, 347 (5): 848-862.
  • [29] Elzaki, T.M. and Ezaki, S.M. (2011). On the connections between Laplace and ELzaki transforms. Advances in Theoretical and Applied Mathematics, 6 (1): 1-10.
  • [30] Almardy, I.A. (2023). The New Integral Transform “Iman Transform”. International Journal of Advanced Research in Science, Communication and Technology, 3 (1): 1-5.
  • [31] Almardy, I.A., Farah, R.A. and Elkeer, M.A. (2023). On the Iman Transform and Systems of Ordinary Differential Equations. International Journal of Advanced Research in Science, Communication and Technology, 3 (1): 577-580.
There are 31 citations in total.

Details

Primary Language English
Subjects Numerical Solution of Differential and Integral Equations
Journal Section Research Articles
Authors

Nihal Özdoğan 0000-0002-7551-1636

Early Pub Date December 12, 2024
Publication Date
Submission Date June 7, 2024
Acceptance Date September 19, 2024
Published in Issue Year 2024Volume: 8 Issue: 2

Cite

APA Özdoğan, N. (2024). Comparison of the results obtained by Iman transform with Laplace transform. Journal of Innovative Science and Engineering, 8(2), 233-242. https://doi.org/10.38088/jise.1497589
AMA Özdoğan N. Comparison of the results obtained by Iman transform with Laplace transform. JISE. December 2024;8(2):233-242. doi:10.38088/jise.1497589
Chicago Özdoğan, Nihal. “Comparison of the Results Obtained by Iman Transform With Laplace Transform”. Journal of Innovative Science and Engineering 8, no. 2 (December 2024): 233-42. https://doi.org/10.38088/jise.1497589.
EndNote Özdoğan N (December 1, 2024) Comparison of the results obtained by Iman transform with Laplace transform. Journal of Innovative Science and Engineering 8 2 233–242.
IEEE N. Özdoğan, “Comparison of the results obtained by Iman transform with Laplace transform”, JISE, vol. 8, no. 2, pp. 233–242, 2024, doi: 10.38088/jise.1497589.
ISNAD Özdoğan, Nihal. “Comparison of the Results Obtained by Iman Transform With Laplace Transform”. Journal of Innovative Science and Engineering 8/2 (December 2024), 233-242. https://doi.org/10.38088/jise.1497589.
JAMA Özdoğan N. Comparison of the results obtained by Iman transform with Laplace transform. JISE. 2024;8:233–242.
MLA Özdoğan, Nihal. “Comparison of the Results Obtained by Iman Transform With Laplace Transform”. Journal of Innovative Science and Engineering, vol. 8, no. 2, 2024, pp. 233-42, doi:10.38088/jise.1497589.
Vancouver Özdoğan N. Comparison of the results obtained by Iman transform with Laplace transform. JISE. 2024;8(2):233-42.
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