Abstract
We discuss the introduction and study of the nabla discrete Mahgoub transform along with its defining properties. The transform of fractional sums and fractional differences are derived, demonstrating the applicability of the transform from the computational viewpoint. Employing the transform, fractional difference equations with initial value problems are solved, thereby enhancing the knowledge of their closed forms. As a side-effect of the Mahgoub-transforms, an attractive connection is established, showing that the discrete Mittag-Leffler function acts as the eigenfunction for the Caputo-type fractional difference operator nabla. These results strengthen the core basis for fractional calculus and herald industrial applications in various science and engineering fields.
Recommended Citation
Gunasekar, Tharmalingam; Udhayasankar, Periyasamy; Raghavendran, Prabakaran; and Kumar, Kamalendra
(2025).
(SI15-120) Exploring Fractional Difference Equations and their Applications with Mahgoub-Transform,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 20,
Iss.
4, Article 14.
Available at:
https://digitalcommons.pvamu.edu/aam/vol20/iss4/14