Infinitesimal prolongations for mixed Ψ-Hilfer operators and applications

In this study, we discuss the infinitesimal prolongation to mixed Ψ Ψ -Hilfer derivative and Ψ Ψ -Riemann Liouville derivative. The prolongation formula for the Ψ Ψ -Riemann Liouville derivative is illustrated using the generalized fractional Burgers-KdV equation, which has particular cases, like the fractional Harry-Dym equation and the fractional Modified Burgers-KdV equation with variable coefficients in the ψ ψ -Riemann Liouville sense. Using the obtained Lie point symmetries, we constructed exact solutions of the fractional differential equations in the ψ ψ -Riemann-Liouville sense wherever possible.