... to derive both approximate and exact solutions to FDEs. This study explores the numerical solutions of the time-fractional Good Boussinesq (TFGB) equation, defined by using the Caputo fractional derivative. Numerical solutions are obtained by employing two distinct and efficient methods: the radial...

... grassland competition model is formulated using the Caputo fractional derivative of order ρ ∈ (0, 1]. The qualitative behavior of the system is analyzed by establishing the non-negativity and boundedness of solutions, followed by a stability analysis of the equilibrium points. Numerical simulations...

... Licensed re-use rights only Murray equation Laplace-residual power series Caputo fractional derivative Taif University TU-DSPP-2024-73 Funding: This research was funded by Taif University, Saudi Arabia (Project No. TU-DSPP-2024-73). In the last few years, it has been...

... of the presented algorithm is to combine Bernoulli polynomials approximation with Caputo fractional derivative and numerical integral transformation to reduce the studied two-dimensional nonlinear Volterra-Fredholm integral equations and fractional integro-differential equations to easily solved algebraic...

... Hirota–Satsuma coupled KdV (HS-cKdV) equations. Design/methodology/approach The proposed technique q-HASTM is the graceful amalgamations of q-homotopy analysis method with Sumudu transform via Caputo fractional derivative, whereas RPSM depend on generalized formula of Taylors series along...