Adomian decomposition method Atangana-Baleanu derivative Bernoulli sub-equation function method Burgers’ equation Caputo derivative Caputo fractional derivative Dirichlet and Neumann boundary conditions Elazki transform Hilfer fractional derivative Laplace transform Laplace transforms Lorenzo-Hartely function Riemann–Liouville fractional integral operator Sumudu transform Volterra-type fractional integro-differential equation caputo fractional derivative chaotic finance complex solution constant proportional Caputo derivative contour surface equilibrium point error estimate fixed point theory fractional calculus fractional differential equations fractional generalized biologic population fractional integral fractional kinetic equation generalized Lauricella confluent hypergeometric function harvesting rate