Higher-order conformable derivatives and their applications
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Keywords:
Higher-Order Conformable derivative, Higher-Order Conformable Laplace transform, Higher-Order Conformable Sumudu.Abstract
After presenting some results and introducing a new definition of the higher-order conformable derivative, we discuss how these findings relate to a novel idea: The higher-order conformable Laplace transform and the higher-order conformable Sumudu transform.
References
F. Alrawajeh Z. Al-Zhouri, N. Al-Mutai, and R. Alkhasawnh. New results on conformable fractional sumudo transform. Theories and applications, International Journal of Analysis and Applications, 17(6):1019–1033, 2019.
R. Bahloul, R.M. Soufiane, T. Abdeljawad, and B. Abdalla: Some Results of Conformable Fourier Transform. European Journal of Pure and Applied Mathematics, Vol. 17, No. 4, (2024), 2405–2430.
R. Bahloul and M. Sbabheh, Some results of the new definition of F α -Fourier transform and their applications. Gulf Journal of Mathematics Vol 19, Issue 2 (2025) 228–246.
R. Bahloul, R. Houssame and A. Thabet, New Definition of F α -Laplace Conformable Transform and Their Applications. Journal of Computational Analysis and Applications Vol. 34, No. 4 (2025), 730–746.
M. Bouziani, R. Houssame and R. Bahloul, Conformable ARA Transform Function and its Properties. Asia Pac. J.Math. 2025 12:58.
M. Caputo, Linear models of dissipation whose q is almost frequency independent-ii. Geophysical J. of the Royal Astronomical Society. (1967); 13(5):529–539.
I. Kadria, M. Horanib, and R. Khali, Solution of a fractional Laplace type equation in a conformable sense using fractional Fourier series with separation of variables technique, Results in Nonlinear Analysis 6 (2023) No. 2, 53–59.
A. Kilic Man, H. Eltayeb, and Kamatan, A Note on the Comparison Between Laplace and Sumudu Transforms. Bulletin of the Iranian Mathematical Society Vol. 37 No. 1 (2011), pp. 131–141.
KS. Killer, B. Ross. An Introduction to the Fractional Calculus and Fractional Differential Equations. New York: John Wiley and Sons (1993).
JT. Machado, V. Kiryakova, F. Mainardi. Recent history of fractional calculus. Communications in Nonlinear Science and Numerical Simulation. (2011); 16(3):1140–1153.
V.T. Nguyen, Note on the convergence of fractional conformable diffusion equation with linear source term, Results in Nonlinear Analysis 5(2022) No. 3, 387–392.
M. Riesz, L'intégrale de Riemann-Liouville et le problème de Cauchy. Acta Mathematica. (1949) ; 81(1) : 1–222.
KH. Roshdi, M. Al Horani, A. Yousef, M. Sababheh. A new definition of fractional derivative, J. Comput. Appl. Math.264 (2014) 65–70.
F.S. Silva, Davidson M. Moreira, and Marcelo A. Moret, Conformable Laplace Transform of Fractional Differential Equations; Axioms 2018, 7, 55.
V. Stojiljkovic, A New Conformable Fractional Derivative and Applications. Sel.Mat. (2022), 9, 370–380.
A. Thabet, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015) 57–66.
H. Zhou, S. Yang, S. Zhang, Conformable derivative approach to anomalous diffusion, Physica A: Stat. Mech. Appl. 491 (2018) 1001–1013.
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