Fractional Kinetic Equations Associated with Generalized Hurwitz-Lerch-Zeta Function

This study examines Jacobi and related integral transforms connected to the generalized Hurwitz–Lerch–Zeta function. We obtain a number of exceptional examples involving Legendre and Gegenbauer transforms. The Riemann–Liouville fractional integral operator and the Elzaki transform are used to find accurate solutions of generalized fractional kinetic equations in terms of generalized Mittag–Leffler functions. We build and investigate three generalized fractional kinetic models. Larger fractional orders result in faster stabilization, while smaller fractional orders cause slower decay because of memory effects, according to graphical analysis for the physically significant domain \((t\ge 0)\) .