An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process

A mathematical model of the movement of the shoreline in a sedimentary ocean basin is discussed. The model includes space–time fractional derivative in Caputo sense and variable latent heat term. An approximate solution of the problem is obtained by Adomian decomposition method and the results thus obtained are compared graphically with an exact solution of integer order (β =1, α= 1). Three particular cases, the standard diffusion, the time-fractional and the spacefractional diffusions are also discussed. The model and solution are generalization of previous works.