A new local fractional modified Benjamin–Bona–Mahony equation is proposed within the derivative in this study for first time. By defining some elementary functions via Mittag–Leffler function (MLF) on Cantor sets (CSs), a set of nonlinear ordinary differential equations (NLFODEs) constructed. Then, fast algorithm namely Yang’s special method employed to find non-differentiable (ND) exact soluti...

In this article, the generalized Jacobi elliptic function expansion method with four new functions was used to fractional (3 + 1)-dimensional Kadomtsev–Petviashvili (GFKP) equation Atangana-Baleanu-Riemann derivative, and abundant types of analytical solutions GFKP were obtained. It is well known that there a tight connection between symmetry travelling wave solutions. Most existing techniques ...

In this paper, new estimates of the sequential Caputo fractional derivatives a function at its extremum points are obtained.We derive comparison principles for linear differential equations, then apply these to obtain lower and upper bounds solutions nonlinear equations. The principle is applied show that initial-boundary-value problem anomalous diffusion admits most one classical solution depe...

The main objective of this work is to present a modification the Mittag- Leffler function deduce relatively new analytical approximate method (for short MMLFM) able solve time-fractional nonlinear partial differential equations (PDEs). Moreover, we employ MMLFM coupled Korteweg-de Vries (KdV) model described by two fractional (FPDEs) based upon Caputo derivative (CFD). simulation projected resu...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Partial differential equations (PDEs) have been successful for solving many problems in computer vision. However, the existing PDEs are all crafted by people with skill, based on some limited and intuitive considerations. As a result, the designed PDEs may not be able to handle complex situations in real applications. Moreover, human intuition may not apply if the vision task is hard to describ...

We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models, Burgers’ equation, the Navier-Stokes equations, the surface quasi-geostrophic equations and the Keller-Segel model for chemotaxis. Here we establish a Petrowsky typ...

We prove a local in time existence and uniqueness theorem of classical solutions of the coupled Einstein–Euler system, and therefore establish the well posedness of this system. We use the condition that the energy density might vanish or tends to zero at infinity and that the pressure is a certain function of the energy density, conditions which are used to describe simplified stellar models. ...

We study Sobolev-type metrics of fractional order on the group of compactly supported diffeomorphisms Diffc(M), where M is a Riemannian manifold of bounded geometry. We prove that the geodesic distance, induced by the Riemannian metric, vanishes if the order s satisfies 0 ≤ s < 1 2 . For M 6= R we show the vanishing of the geodesic distance also for s = 1 2 , and for dim(M) = 1 we show that the...