New Efficient Computations with Symmetrical and Dynamic Analysis for Solving Higher-Order Fractional Partial Differential Equations

Due to the rapid development of theoretical and computational techniques in recent years, role nonlinearity dynamical systems has attracted increasing interest been intensely investigated. A study nonlinear waves shallow water is presented this paper. The classic form Korteweg–de Vries (KdV) equation based on oceanography theory, sea, internal ion-acoustic plasma. fluid assumption shown framework by a sequence fractional partial differential equations. Indeed, primary purpose use semi-analytical technique Fractional Taylor Series achieve numerical results for fifth-order KdV models non-integer order. Caputo operator used dealing with derivatives. generated solutions order modeling turbulence processes field ocean engineering are compared analytically numerically, demonstrate behaviors several parameters current model. We verified method’s convergence analysis provided an error estimate showing 2D 3D graphs further confirm its efficacy.