A novel eight-parameter Mittag-Leffler function: Construction, analytical properties, and applications in fractional differential equations
Mohit Khatikmohitkhatikmkvp@gmail.comDepartment of MathematicsPacific Academy of Higher Education and Research UniversityUdaipur, Rajasthan, 313002, India0009-0007-9879-7917View full profile → , Abhilasha Meenaabhimeena2601@gmail.comDepartment of MathematicsPacific Academy of Higher Education and Research UniversityUdaipur, Rajasthan, 313002, India0009-0006-7449-6768View full profile → , *Naresh MenariaCorresponding authornaresh.menaria14@gmail.comDepartment of MathematicsPacific Academy of Higher Education and Research UniversityUdaipur, Rajasthan, 313002, India0009-0009-0937-3982View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2699
- Pages:
- 2627–2635
Abstract
We propose a comprehensive study of the generalized eight-parameter Mittag-Leffler (8P-ML) function and its operational properties under various fractional calculus operators. Explicit results are derived for its integer and fractional-order derivatives, integrals, Laplace and Fourier transforms, and convolution identities. These findings extend classical Mittag- Leffler (M-L) theory and provide foundational tools for applications in anomalous diffusion, viscoelastic modeling, and fractional dynamic systems. The results are presented in a unified framework, offering deeper insights into the structural behavior of this highly generalized function.
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References
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