A Revised Kamal Integral Transformation Method for Solving First-Order Nonlinear Fractional Differential Equations
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Page Numbers:
1593-1612
Digital Object Identifier:
10.58578/yasin.v5i3.5366
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Authors:
Nura Uba1, M. M. Adamu2, M. Abdulhameed3, Hafsat Y. U4, Okai J. O5* 
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Abstract
This study integrates the Kamal transform method with Adomian polynomials to provide approximate analytical solutions for non-linear fractional differential equations. Since the Kamal transform alone cannot handle non-linear terms, Adomian polynomials are used to decompose these terms. The resulting solutions are compared with those from other methods applied to the same problems. The results show that the solution obtained with the Kamal transform and Adomian polynomial closely aligns with those from other methods, demonstrating the effectiveness of this combined approach. This work emphasizes the strength of the Kamal transform method and Adomian polynomials as integral transform techniques for solving non-linear equations.
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References
Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers.
Diethelm, K., Ford, N. J., & Freed, A. D. (2002). A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 29(1-4), 3-22.
Elzaki, T. M. (2011). The new integral transform “Elzaki transform.” Global Journal of Pure and Applied Mathematics, 7(1), 57–64.
Ghanwat, A. J., & Gaikwad, S. B. (2022). Application of Kamal Transform for Solving Linear Volterra Integral Equations of Second Kind. Journal of Emerging Technologies and Innovative Research, 9(4), 7–14.
Hussain, E. A., & Jasim, A. S. (2021). Z-transform solution for nonlinear difference equations. Al-Mustansiriyah Journal of Science, 32(4), 51–56. https://doi.org/10.23851/mjs.v32i4.1019
Janolkar, M. M. (2018). Solution of Ordinary Differential Equations with variable coefficients using Kamal Transform. International Journal of Scientific Research and Review, 7(3), 173–178.
Kamal, A. H. M., &Hosseini, K. (2017). An analytical approach to fractional-order differential equations using Kamal integral transform. Computers & Mathematics with Applications, 73(10), 2031-2044.
Khandelwal, R., Kumawat, P., & Khandelwal, Y. (2018). Kamal decomposition method and its application in solving coupled system of nonlinear PDE’s. Malaya Journal of Matematik, 06(03), 619–625. https://doi.org/10.26637/mjm0603/0024
Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations (Vol. 204). Elsevier.
Mushtt, I. Z. (2023). A Novel Integral Transform : INEM - Transform. Journal of Kufa for Mathematics and Computer, 10(2), 109–113.
Odetunde, O. S., & Taiwo, O. A. (2014). A Decomposition Algorithm for the Solution of Fractional Quadratic Riccati Differential Equations with Caputo Derivatives. American Journal of Computational and Applied Mathematics, 4(3), 83–91. https://doi.org/10.5923/j.ajcam.20140403.03
Opanuga, A. A., Edeki, S. O., Okagbue, H. I., & Akinlabi, G. O. (2015). A novel approach for solving quadratic Riccati differential equations. International Journal of Applied Engineering Research, 10(11), 29121–29126.
Owolabi, J. A., & Oderinu, R. A. (2021). Kamal Transform Based Analytical Solution of a Generalized Nonlinear Hirota-Satsuma Coupled Equations 2 Properties of Kamal Transform. Asian Journal of Pure and Applied Mathematics, 3(1), 69–78.
Rustam, Z. R., & Sulaiman, N. A. (2023). Kamal transform technique for solving system of linear Volterra integro-differential equations of the second kind. Polytechnic Journal, 12(2), 6–16. https://doi.org/10.25156/ptj.v12n2y2022.pp6-16
Sedeeg, A. K. . H. (2016). The New Integral Transform’ Kamal Transform’. Advances in Theoretical and Applied Mathematics, 11(4), 451–458.
Shah, R., Khan, H., Kumam, P., Arif, M., & Baleanu, D. (2019). Natural transform decomposition method for solving fractional-order partial differential equations with proportional delay. MDPI, 7(6), 1–14. https://doi.org/10.3390/MATH7060532