Journals Information
Universal Journal of Applied Mathematics Vol. 13(3), pp. 35 - 47
DOI: 10.13189/ujam.2025.130301
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Analytical Solution of the Time-Fractional Telegraph Equation in a Whole Space-Domain and Half-Domain Using the Mamadu Integral Transform and Inverse Fourier Transform
Ebimene James Mamadu 1,*, Jude Chukwuyem Nwankwo 2, Ebikonbo-Owei Anthony Mamadu 1,3, Irerhievwie Oghenetega Stephen 4, Henrietta Ify Ojarikre 1, Ignatius Nkonyeasua Njoseh 1, Jonathan Tsetimi 1
1 Department of Mathematics, Delta State University, Abraka, Nigeria
2 Department of Mathematics, University of Delta, Agbor, Nigeria
3 Department of Mathematics, Michael and Cecilia Ibru University, Agbara-Otor, Delta State, Nigeria
4 Department of General Studies, Petroleum Training Institute, Effurun, Delta State, Nigeria
ABSTRACT
The description of memory effects in wave propagation and anomalous diffusion is best analyzed using the time-fractional telegraph equation (TFTE), widely applicable in fluid flow, signal transmission, and biological systems. In this paper, the analytic solution of TFTE in the whole space-domain and in a half-domain is investigated using the Mamadu integral transform. For a reliable and accurate representation of hereditary and nonlocal properties in TFTE, the fractional derivatives are defined in the Caputo sense. The Mamadu Transform converts the problem into an algebraic equation to ease the solution process. The contour integration is then employed to compute the inverse Mamadu Transform, where the solution structure is determined at the poles of the transformed function via the residue theorem. Additionally, the spatial characteristics of the solution are reconstructed through the inverse Fourier transform, ensuring an adequate representation in the transformed domain. Using specific values for the parameters 伪,尾,a,b and c, we analyze the system response by evaluating the resulting characteristic equation. The results depict the effectiveness of the Mamadu Transform, in conjunction with the inverse Fourier transform for solving the TFTE, offering systematic and flexible techniques to handle diverse problems in a complex domain.
KEYWORDS
Mamadu Integral Transform, Inverse Fourier Transform, Contour Integration, Residue Theorem, Fractional Telegraph Equation, Caputo Fractional Derivative
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ebimene James Mamadu , Jude Chukwuyem Nwankwo , Ebikonbo-Owei Anthony Mamadu , Irerhievwie Oghenetega Stephen , Henrietta Ify Ojarikre , Ignatius Nkonyeasua Njoseh , Jonathan Tsetimi , "Analytical Solution of the Time-Fractional Telegraph Equation in a Whole Space-Domain and Half-Domain Using the Mamadu Integral Transform and Inverse Fourier Transform," Universal Journal of Applied Mathematics, Vol. 13, No. 3, pp. 35 - 47, 2025. DOI: 10.13189/ujam.2025.130301.
(b). APA Format:
Ebimene James Mamadu , Jude Chukwuyem Nwankwo , Ebikonbo-Owei Anthony Mamadu , Irerhievwie Oghenetega Stephen , Henrietta Ify Ojarikre , Ignatius Nkonyeasua Njoseh , Jonathan Tsetimi (2025). Analytical Solution of the Time-Fractional Telegraph Equation in a Whole Space-Domain and Half-Domain Using the Mamadu Integral Transform and Inverse Fourier Transform. Universal Journal of Applied Mathematics, 13(3), 35 - 47. DOI: 10.13189/ujam.2025.130301.