Resumen
En este trabajo se introduce una nueva transformada de Laplace fraccionaria denominada transformada doble de Laplace non-conformable generalizada. Esta propuesta extiende las transformadas dobles de Laplace non-conformable mediante la inclusión de funciones moduladoras generalizadas ϕ(u) y ψ(v). Se establecen las propiedades básicas de la transformada, incluida la linealidad, las condiciones de existencia, las propiedades derivativas y los teoremas de convolución. Por último, la transformada doble de Laplace non-conformable generalizada (Generalized Non-Conformable Double Laplace Transform - NCGDT) se aplica a la resolución de diferentes tipos de ecuaciones diferenciales parciales fraccionarias non-conformables.
Referencias
Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279:57–66. https://doi.org/10.1016/j.cam.2014.10.016.
Abdeljawad, T., Younus, A., Alqudah, M. A., and Atta, U. (2023). On fuzzy conformable double laplace transform with applications to partial differential equations. Computer Modeling in Engineering and Sciences, 134:2163–2191. https://doi.org/10.32604/cmes.2022.020915.
Al-Rab’a, A., Al-Sharif, S., and Al-Khaleel, M. (2022). Double conformable sumudu transform. Symmetry, 14:2249. https://doi.org/10.3390/sym14112249.
Alawad, F. A., Yousif, E. A., and Arbab, A. I. (2013). A new technique of laplace variational iteration method for solving space time fractional telegraph equations. International Journal of Differential Equations, pages 256593–256603. https://doi.org/10.1155/2013/256593.
Alfaeih, S., Bakcioglu, G., and Misirli, E. (2021). Conformable double sumudu transform with applications. Journal of Applied and Computational Mechanics, 7(2):578–586. https://doi.org/10.22055/JACM.2020.35315.2625.
Alfaeih, S. and Misirli, E. (2021). Conformable double laplace transform method for solving conformable fractional partial differential equations. Computational Methods for Differential Equations, 9(3):908–918. https://doi.org/10.22034/cmde.2020.38135.1678.
Anastassiou, G. A. (2011). Advances on Fractional Inequalities. Springer. https://doi.org/10.1007/978-1-4614-0703-4.
Atangana, A. and Baleanu, D. (2015). New properties of conformable derivatives. Open Mathematics, 13:889–898. https://doi.org/10.1515/math-2015-0081.
Avci, J. D., Iskender, E., and Ozdemir, N. (2017). Conformable heat equation on a radial symmetric plate. Thermal Science, 21:819–826. https://doi.org/10.2298/TSCI160427302A.
Deresse, A. T. (2022). Analytical solutions to two-dimensional nonlinear telegraph equations using the conformable triple laplace transform iterative method. Advances in Mathematical Physics, 1:4552179. https://doi.org/10.1155/2022/4552179.
Diethelm, K. (2010). The Analysis of Fractional Differential Equations. Springer. https://link.springer.com/book/10.1007/978-3-642-14574-2.
Doetsch, G. (2012). Introduction to the Theory and Application of the Laplace Transformation. Springer Science and Business Media. https://link.springer.com/book/10.1007/978-3-642-65690-3.
González, F., Mohammed, P. O., and Nápoles Valdes, J. (2020). Nonconformable fractional laplace transform. Kragujevac Journal of Mathematics, 46:341–354. https://doi.org/10.46793/KgJMat2203.341M.
Gozutok, N. Y. and Gozutok, U. (2018). Multivariable conformable fractional calculus. Filomat, 32(1):45–55. https://doi.org/10.2298/FIL1801045G.
Guzmán, P., Langton, G., Lugo Motta Bittencurt, L., Medina, J., and Nápoles Valdes, J. (2018). A new definition of a fractional derivative of local type. Journal of Mathematical Analysis, 9(2):88–98. http://www.ilirias.com/jma/repository/docs/JMA9-2-9.pdf.
Hashemi, M. S. (2018). Invariant subspaces admitted by fractional differential equations with conformable derivatives. Chaos, Solitons & Fractals, 107:161–169. https://doi.org/10.1016/j.chaos.2018.01.002.
Honggang, J. and Yanmin, Z. (2022). Conformable double laplace–sumudu transform decomposition method for fractional partial differential equations. Complexity, 1:7602254. https://doi.org/10.1155/2022/7602254.
Injrou, S. and Hatem, I. (2022). Solving some partial differential equations by using double laplace transform in the sense of nonconformable fractional calculus. Mathematical Problems in Engineering, 2022:1–10. https://doi.org/10.1155/2022/5326132.
Jarrín, H. D., Marcillo-Parra, J. L., Velasco-Velasco, J., and Vivas-Cortez, M. (2026). Una variación de la transformada doble de laplace non-conformable. Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, 50(194):213–233. https://doi.org/10.18257/raccefyn.3288.
Khalil, R., Al Horani, M., Yousef, A., and Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264:65–70. https://doi.org/10.1016/j.cam.2014.01.002.
Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier. https://shop.elsevier.com/books/theory-and-applications-of-fractional-differential-equations/kilbas/978-0-444-51832-3.
Martínez, F., Mohammed, P. O., and Nápoles Valdes, J. E. (2022). Nonconformable fractional laplace transform. Kragujevac Journal of Mathematics, 46(3):341–354. https://doi.org/10.46793/KgJMat2203.341M.
Meddahi, M., Jafari, H., and Yang, X.-J. (2021). Towards new general double integral transform and its applications to differential equations. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.7898.
Mohamed, M. Z., Hamza, A. E., and Sedeeg, A. K. H. (2023). Conformable double sumudu transformations and efficient approximate solutions to the fractional coupled burger’s equation. Ain Shams Engineering Journal, 14(3):101879. https://doi.org/10.1016/j.asej.2022.101879.
Nápoles Valdes, J., Guzmán, P., and Lugo, L. (2018). Some new results on nonconformable fractional calculus. Advances in Dynamical Systems and Applications, 13(2):167–175. https://www.ripublication.com/adsa18/v13n2p5.pdf.
Ross, B., Samko, S., and Love, E. R. (1994). Functions that have no first order derivative might have fractional derivatives of all order less than one. Real Analysis Exchange, 20(2):140–157. https://es.scribd.com/document/698712785/44152475.
Sedeeg, A. H. (2016). The new integral transform “kamal transform”. Advances in Theoretical and Applied Mathematics, 11:451–458. https://www.ripublication.com/atam16/atamv11n4_14.pdf.
Sedeeg, A. K. H. and Alhamad, A. (2025). Conformable general double transform and its applications for solving conformable partial differential equations. Sohag Journal of Mathematics, 12(2):1–17. http://dx.doi.org/10.18576/sjm/120201.
Vivas-Cortez, M., Nápoles, J. E. N., Hernández, J. E., Velasco, J., and Larreal, O. (2021). On nonconformable fractional laplace transform. Applied Mathematics, 15(4):403–409. https://doi.org/10.18576/amis/150401.
Vivas-Cortez, M., Velasco, J., and Jarrín, H. D. (2025). A new generalized local derivative of two parameters. Applied Mathematics and Information Sciences, 19(3):713–723. https://doi.org/10.18576/amis/190319.
Watugala, G. K. (1993). Sumudu transform: A new integral transform to solve differential equations and control engineering problems. International Journal of Mathematical Education in Science and Technology, 24:35–43. https://doi.org/10.1080/0020739930240105.
Yang, X.-J., Baleanu, D., and He, J.-H. (2013). Transport equations in fractal porous media within fractional complex transform method. Proceedings of the Romanian Academy Series A, 14(4):287–292. https://acad.ro/sectii2002/proceedings/doc2013-4/04-Baleanu.pdf.
Özkan, O. and Kurt, A. (2018). On conformable double laplace transform. Optical and Quantum Electronics, 50:1–9. https://doi.org/10.1007/s11082-018-1372-9.
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