| Paper title: |
The A–Variational Iteration Transform |
| Published in: | Issue 1, (Vol. 19) / 2025 |
| Publishing date: | 2025-04-15 |
| Pages: | 22-27 |
| Author(s): | HASAN Arkan Sh. |
| Abstract. | In this paper, a new integral transform called A–Transform is introduced and studied. Some properties and Theorems have been discussed to demonstrate its valid. In addition, another new combined method based on the A–Transform and the Variational Iteration method called A– Variational Iteration Transform, shortly (AVIT) is introduced and studied as well. This combined method gives us a new correction functional for differential or integrodifferential equation in terms of A–Transform, and that make it easy to use for solving problems. Some examples have been delt with the AVIT Method such as Volterra integral and Integrodifferential Equations of the second kind. |
| Keywords: | A–Transform, Variational Iteration Method, A- Variational Iteration Transform, Volterra Integral, And Integrodifferential Equations. |
| References: | 1. Butris, Raad & Raad Noori, Noori. (2022). A study in the existence and uniqueness of Volterra-Fredholm integro- differential equations. Journal of Applied Computer Science & Mathematics. 16. 26-30.10.4316/JACSM.202202004 2. Shareef, Arkan & Dosky, Sizar. (2022). Numerical Solution of Volterra Integral Equations with a Weakly Singular Kernel Using the Seventh Order Non-Polynomial Spline Function Method. Journal of Applied Computer Science & Mathematics. 16. 24-29. 10.4316/JACSM.202201004. 3. Shareef, Arkan & Dosky, Sizar. (2022). Two analytic methods for solving the Volterra integral equations with a weakly singular kernel. 4. Jafari, Hossein. (2020). A new approach for solving nonlinear Volterra integro-differential equations with Mittag--Leffler kernel. Proceedings of the Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan. 46. 144-158. 10.29228/proc.24. 5. Khalid, Muhammad & Sultana, Mariam & Zaidi, Faheem & Arshad, Uroosa. (2015). Application of Elzaki Transform Method on Some Fractional Differential Equations. Mathematical Theory and Modeling. 5. 89-96. 6. Aggarwal, Sudhanshu & Bhatnagar, Kavita & Dua, Arti. (2019). Dualities between Elzaki Transform and Some Useful Integral Transforms. International Journal of Innovative Technology and Exploring Engineering. 8. 2278-3075. 10.35940/ijitee.L2729.1081219. 7. Aggarwal, Sudhanshu & Sharma, Nidhi & Chauhan, Raman. (2018). Application of Kamal Transform for Solving Linear Volterra Integral Equations of First Kind. 6. 2081-2088. 8. Aggarwal, Sudhanshu & Sharma, Nidhi & Chauhan, Raman. (2020). Duality relations of Kamal transform with Laplace, Laplace–Carson, Aboodh, Sumudu, Elzaki, Mohand and Sawi transforms. SN Applied Sciences. 2. 10.1007/s42452-019-1896-z. 9. Higazy, Mahmoud & Aggarwal, Sudhanshu. (2021). Sawi transformation for system of ordinary differential equations with application. Ain Shams Engineering Journal. 12. 3173-3182. 10.1016/j.asej.2021.01.027. 10. Tarig, Elzaki. (2011). The new integral transform "Elzaki transform". Global Journal of Pure and Applied Mathematics. 7. 57-64. 11. Song, Y. & Kim, Hwajoon. (2014). The solution of Volterra integral equation of the second kind by using the Elzaki transform. Applied Mathematical Sciences. 8. 525-530. 10.12988/ams.2014.312715. 12. Anjum, Naveed & He, Ji-Huan. (2019). Laplace transform: Making the variational iteration method easier. Applied Mathematics Letters. 92. 10.1016/j.aml.2019.01.016. 13. Naveed Khan, Muhammad & Haider, Jamil & Wang, Zhentao & Lone, Showkat & Almutlak, Salmeh & El- seesy, Ibrahim. (2023). Application of Laplace-based variational iteration method to analyze generalized nonlinear oscillations in physical systems. Modern Physics Letters B. 37. 10.1142/S0217984923501695. 14. Rani, Dimple & Mishra, Vinod. (2019). Solutions of Volterra Integral and Integro-differential Equations using Modified Laplace Adomian Decomposition Method. Journal of Applied Mathematics, Statistics and Informatics. 15. 5-18. 10.2478/jamsi-2019-0001. 15. He, Ji-Huan & Wu, Xu-Hong. (2007). Variational Iteration Method: New Development and Applications. Computers & Mathematics with Applications. 54. 881-894. 10.1016/j.camwa.2006.12.083. 16. Wazwaz, Abdulmajid, "Linear and nonlinear integral equations .," Berlin: Springer., vol. 639, 2011. |
| Back to the journal content | |
