We use a new integral transform approach to solve the fractional Harry Dym equation and Rosenau-Hyman in this work. The Elzaki transformation are combined suggested method (ET). To handle two nonlinear problems, we first construct transforms of Caputo derivative (CFD) Atangana-Baleanu (ABFD). ultimate purpose study is find an error analysis that demonstrates our final result converges exact app...

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and modified Vries-Burgers equations on a bounded domain. Sufficient conditions blowing-up solutions in finite time aforementioned are presented. We also discuss maximum principle influence grad...

We consider a chain of elastic beads subjected to vanishingly weak loading conditions, i.e., the beads are barely in contact. The grains repel upon contact via the Hertz-type potential, Vinfinitydelta(n), n>2, where delta> or =0, delta being the grain-grain overlap. Our dynamical simulations build on several earlier studies by Nesterenko, Coste, and Sen and co-workers that have shown that an im...