Inverse laplace transform for a new class of functions and its application to time-fractional diffusion-wave equations

• Autorzy: Latif Mohamed S. Abdel , Elhadedy Hager , Kader Abass H. Abdel

Identyfikatory

DOI

10.17512/jamcm.2024.4.05

• Języki publikacji: EN

Abstrakty

EN

This paper investigates the inverse Laplace transform of a certain class of functions. This inverse Laplace transform is obtained in the form of an infinite series of the three-parameter Mittag-Leffler function. Additionally, we found the sum of an infinite series of Mittag-Leffler functions with three parameters in terms of the Wright function. As an application, we get an exact solution of the time-fractional diffusion-wave equation with the Hilfer-Prabhakar time-fractional derivative using Laplace and Fourier transforms.

Słowa kluczowe

EN

Mittag-Leffler function; Wright function; Hilfer-Prabhakar derivatives; Laplace transform; Fourier transform; diffusion-wave equation

PL

Funkcja Mittag-Lefflera; funkcja Wrighta; pochodne Hilfera-Prabhakara; transformata Laplace'a; transformata Fouriera; równanie dyfuzji-fali

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 4
• Strony: 56--65
• Opis fizyczny: Bibliogr. 13 poz., rys., tab.

Twórcy

autor

Latif Mohamed S. Abdel

• Department of Mathematics, Faculty of Science, New Mansoura UniversityNew Mansoura City, Egypt
• Department of Mathematics and Engineering Physics, Engineering Faculty Mansoura University, Mansoura, Egypt

autor

Elhadedy Hager

• Department of Mathematics and Engineering Physics, Engineering Faculty Mansoura University, Mansoura, Egypt

autor

Kader Abass H. Abdel

• Department of Mathematics, Faculty of Science, New Mansoura UniversityNew Mansoura City, Egypt
• Department of Mathematics and Engineering Physics, Engineering Faculty Mansoura University, Mansoura, Egypt

Bibliografia

• 1. Ansari, A., & Sheikhani, A.R. (2014). New identities for the Wright and the Mittag-Leffler functions using the Laplace transform. Asian-European Journal of Mathematics, 7(3), 1450038.
• 2. Elhadedy, H., Latif, M.S.A., Nour, H.M., & Kader, A.H.A. (2022). Exact solution for heat conduction inside a sphere with heat absorption using the regularized Hilfer-Prabhakar derivative. Journal of Applied Mathematics and Computational Mechanics, 21(2), 27-37.
• 3. Garra, R., Gorenflo, R., Polito, F., & Tomovski, Z. (2014). Hilfer Prabhakar derivatives and some applications. Applied Mathematics and Computation, 242, 276-589.
• 4. Bokhari, A., Belgacem, R., Kumar, S., Baleanu, D., & Djilali, S. (2022). Projectile motion using three parameter Mittag-Leffler function calculus. Mathematics and Computers in Simulation, 195, 22-30.
• 5. Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations. Elsevier.
• 6. Mainardi, F., Mura, A., & Pagnini, G. (2010). The M-Wright function in time-fractional diffusion processes: A tutorial survey. International Journal of Differential Equations, 104505.
• 7. Srivastava, H.M., & Choi, J. (2011). Zeta and q-Zeta Functions and Associated Series and Integrals. Elsevier.
• 8. Sandev, T., & Tomovski, Z. (2019). Fractional Equations and Models. Theory and Applications. Cham: Springer Nature Switzerland AG.
• 9. Korotkov, N.E., & Korotkov, A.N. (2020). Integrals Related to the Error Function. Chapman and Hall/CRC.
• 10. Povstenko, Y. (2015). Linear Fractional Diffusion-wave Equation for Scientists and Engineers. Springer International Publishing.
• 11. Pskhu, A., & Rekhviashvili, S. (2020). Fractional diffusion-wave equation with application in electrodynamics. Mathematics, 8(11), 2086.
• 12. Maimardi, F. (2022). Fractional Calculus and Waves in Linear Viscoelasticity, 2nd Edition. World Scientific.
• 13. Chen, W., Sun, H., & Li, X. (2022). Fractional Derivative Modeling in Mechanics and Engineering.Springer Nature.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).