Fractional Laplace transform for matrix valued functions with applications

References

• Abdeljawad, T. (2015). On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 57–66. doi:10.1016/j.cam.2014.10.016
   Web of Science ®Google Scholar
• Abu Hammad, I., & Khalil, R. (2014). Fractional Fourier series with applications. American Journal of Computational and Applied Mathematics, 4(6), 187–191.
   Google Scholar
• Ahmed, B. (2021). Generalization of fractional Laplace transform for higher order and its application. Journal of Innovative Applied Mathematics and Computational Sciences, 1(1), 79–92.
   Google Scholar
• Ain, Q. T., Anjum, N., Din, A., Zeb, A., Djilali, S., & Khan, Z. A. (2022). On the analysis of Caputo fractional order dynamics of Middle East Lungs Coronavirus (MERS-CoV) model. Alexandria Engineering Journal, 61(7), 5123–5131. doi:10.1016/j.aej.2021.10.016
   Web of Science ®Google Scholar
• Ain, Q. T., Anjum, N., & He, C. H. (2021). An analysis of time-fractional heat transfer problem using two-scale approach. GEM-International Journal on Geomathematics, 12(1), 1–10.
   Web of Science ®Google Scholar
• Al Horani, M., Hammad, M. A., & Khalil, R. (2016). Variation of parameters for local fractional nonhomogenous linear differential equations. Journal of Mathematics and Computer Science, 16(2), 147–153. doi:10.22436/jmcs.016.02.03
   Google Scholar
• ALHorani, M., & Khalil, R. (2018). Total fractional differentials with applications to exact fractional differential equations. International Journal of Computer Mathematics, 95(6–7), 1444–1452. doi:10.1080/00207160.2018.1438602
   Web of Science ®Google Scholar
• Al-Horani, M., Khalil, R., & Aldarawi, I. (2020). Fractional Cauchy Euler differential equation. Journal of Computational Analysis and Applications, 28(2), 226–233.
   Google Scholar
• Al-Zhour, Z., Alrawajeh, F., Al-Mutairi, N., & Alkhasawneh, R. (2019). New results on the conformable fractional Sumudu transform: Theories and applications. International Journal of Analysis and Applications, 17(6), 1019–1033.
   Web of Science ®Google Scholar
• Anderson, D. R., Camrud, E., & Ulness, D. J. (2018). On the nature of the conformable derivative and its applications to physics. Journal of Fractional Calculus and Applications, 10(2), 92–135.
   Google Scholar
• Anjum, N., Ain, Q. T., & Li, X. X. (2021). Two-scale mathematical model for tsunami wave. GEM-International Journal on Geomathematics, 12(1), 1–12.
   Web of Science ®Google Scholar
• Anjum, N., He, C. H., & He, J. H. (2021). Two-scale fractal theory for the population dynamics. Fractals, 29(07), 2150182. doi:10.1142/S0218348X21501826
   Web of Science ®Google Scholar
• Atangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivative. Open Mathematics, 13(1) doi:10.1515/math-2015-0081
   Web of Science ®Google Scholar
• Bouchenak, A. H. M. E. D., Khalil, R., & AlHorani, M. (2021). Fractional Fourier series with separation of variables technique and it’s application on fractional differential equations. WSEAS Transactions on Mathematics, 20, 461–469. doi:10.37394/23206.2021.20.48
   Google Scholar
• Bushnaq, S., Shah, K., Tahir, S., Ansari, K. J., Sarwar, M., & Abdeljawad, T. (2022). Computation of numerical solutions to variable order fractional differential equations by using non-orthogonal basis. AIMS Mathematics, 7(6), 10917–10938. doi:10.3934/math.2022610
   Web of Science ®Google Scholar
• Bushnaque, A., Al-Horani, M., & Khalil, R. (2020). Tensor product technique and atomic solution of fractional Bate Man Burgers equation. Journal of Mathematics and Computer Science, 11(1), 330–336.
   Google Scholar
• Caputo, M., & Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), 73–85.
   Google Scholar
• Chung, W. S. (2015). Fractional Newton mechanics with conformable fractional derivative. Journal of Computational and Applied Mathematics, 290, 150–158. doi:10.1016/j.cam.2015.04.049
   Web of Science ®Google Scholar
• Hammad, M. A., & Khalil, R. (2014). Conformable fractional heat differential equation. International Journal of Pure and Applied Mathematics, 94(2), 215–221.
   Google Scholar
• Hristova, S., Agarwal, R., & O’Regan, D. (2020). Explicit solutions of initial value problems for systems of linear Riemann–Liouville fractional differential equations with constant delay. Advances in Difference Equations, 2020(1), 1–18. doi:10.1186/s13662-020-02643-8
   Google Scholar
• Ilhem, K., Al Horani, M., & Khalil, R. (2022). Solution of non-linear fractional Burger’s type equations using the Laplace transform decomposition method. Results in Nonlinear Analysis, 5(2), 131–151. doi:10.53006/rna.1053470
   Google Scholar
• Khalil, R., Al Horani, M., & Anderson, D. (2016). Undetermined coefficients for local fractional differential equations. Journal of Mathematics and Computer Science, 16(02), 140–146. doi:10.22436/jmcs.016.02.02
   Google Scholar
• Khalil, R., Al Horani, M., Yousef, A., & Sababheh, M. (2014). A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 65–70. doi:10.1016/j.cam.2014.01.002
   Web of Science ®Google Scholar
• Mhailan, M., Hammad, M. A., Horani, M. A., & Khalil, R. (2020). On fractional vector analysis. Journal of Mathematics and Computer Science, 10(6), 2320–2326.
   Google Scholar
• Miller, K. S., & Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. New York: John Wiley and Sons Inc.
   Google Scholar
• Vinh An, T., Vu, H., & Van Hoa, N. (2017). A new technique to solve the initial value problems for fractional fuzzy delay differential equations. Advances in Difference Equations, 2017(1), 1–20. doi:10.1186/s13662-017-1233-z
   Google Scholar
• Younis, J., Ahmed, B., AlJazzazi, M., Al Hejaj, R., & Aydi, H. (2022). Existence and uniqueness study of the conformable Laplace transform. Journal of Mathematics, 2022, 1–7. doi:10.1155/2022/4554065
   Web of Science ®Google Scholar