... 0 C w ( ζ ) = C 7 u ( ζ ) − C 8 v ( ζ ) , w 0 = k 3 , Fractional derivative and integrals q-homotopy analysis transform technique Laplace transform Economic and environmental mathematical model Stability analysis...

... for the Black–Scholes model, which is the most important model in finance. For simulations, homotopy perturbation and the Laplace transform are used and the obtained solutions are expressed in terms of the generalized Mittag-Leffler function (MLF). Design/methodology/approach The homotopy perturbation...

... are solved using a combined BEM and Laplace transform. The time–space dependent coefficient equation is reduced to a time-dependent coefficient equation using an analytical transformation. Then, the time-dependent coefficient equation is Laplace transformed to get a constant coefficient equation, which can...

...) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional...

...; L = operator of Laplace transform; m = parameter for variable heat transfer coefficient; P = constant of initial value; Pe = Peclet number (= LU/α); N_c = dimensionless convection–conductivity parameter...

... is proposed for solving the problem in the Laplace transformation domain. The solution in the physical domain is recovered by a numerical inverse Laplace transformation technique. To treat the double integral over R in using the dual‐reciprocity method described in Brebbia and Nardini (1983...