An extended Mittag Leffler function in terms of extended Wright complex hypergeometric function

2025

Alexandria Engineering Journal, Vol 117, Iss , Pp 364-375 (2025)

Advanced mathematical ideas such as the fractional integral operator and the Mittag-Leffler (M-L) function offer a strong foundation for comprehending complicated systems with memory and fractional dynamics. An epidemiological model that uses fractional derivatives to represent certain non-standard illness patterns. For diseases with a lengthy incubation time or for which “memory” effects impact the recovery process, fractional calculus is ideally suited to simulate processes where the pace of change is contingent upon the system’s history.With the aid of the generalized complex Pochhammer symbol, a novel generalization of the multivariate extended M-L function has been proposed in terms of the extended Wright generalized complex hypergeometric function. Subsequently, the fundamental characteristics of the suggested generalized function are examined. We give two formulas, one for the fractional integral and the other for the differential of the generalized multivariate extended M-L function. Additionally, using the recently described GEMLF, additional fractional integral formulas were defined. Furthermore, we introduced the expanded equations through the application of the generalized extended M-L function in integral transformations, including the Euler-Beta, Mellin, and Laplace transforms. The solution of the fractional Susceptible–Infectious–Recovered (SIR) model for memory-effective infectious diseases has been presented.

article

English

Elsevier, 2025.

Mittag-Leffler, Pochhammer symbol, Extended Beta function, Extended Wright complex Hypergeometric function, Fractional derivatives, Fractional integrals, Engineering (General). Civil engineering (General), TA1-2040