An Efficient Analytical Approach to Investigate Fractional Caudrey–Dodd–Gibbon Equations with Non-Singular Kernel Derivatives

Fractional calculus is at this time an area where many models are still being developed, explored, and used in real-world applications branches of science engineering non-locality plays a key role. Although wonderful discoveries have already been reported by researchers important monographs review articles, there great deal non-local phenomena that not studied only waiting to be explored. As result, we can continually learn about new aspects fractional modelling. In study, precise analytical method with non-singular kernel derivatives solve the Caudrey–Dodd–Gibbon (CDG) model, modification fifth-order KdV equation (fKdV). The derivative taken into account Caputo–Fabrizio (CF) Atangana–Baleanu Caputo sense (ABC). This model illustrates propagation magneto-acoustic, shallow-water, gravity–capillary waves plasma medium. dynamic behaviour acquired solutions has represented number two- three-dimensional figures. A simulations also performed demonstrate how resulting physically behave respect order. significance current research obtained using strong approach. Utilizing operator equivalent another benefit results present work similar symmetry partial differential equations.