Abstract: In this paper, we establish some sufficient conditions for the existence and nonexstence of positive solutions to a general class of higher-order nonlinear fractional differential equation. The results are established by converting the problem into an equivalent integral equation and applying Banach fixed point theorem, nonlinear differentiation of Leray-Schauder type and the fixed po...

A nonlinear integral-differential equation describing the cellular front of an overdriven detonation is obtained by an analysis carried out in the neighborhood of the instability threshold. The analysis reveals both an unusual mean streaming motion, resulting from the rotational part of the oscillatory flow, and pressure bursts generated by the crossover of cusps representative of Mach stems pr...

Velocity estimation using tracer conservation or heat flow equation based on infrared image sequence is one of the most challenging inverse problems in geosciences and remote sensing applications. In this paper, a new nonlinear model has been created for estimating top surface velocity from an infrared image sequence. The differential form of tracer conservation or heat flow equation is replace...

Abstract We consider a nonlinear parabolic equation in one space variable, satisfying a three point boundary condition, such as the heat equation when the temperature at the end is controlled by a sensor at the the point η. We show that the integral solution, in the space of continuous functions satisfying the boundary values, converges to the equilibrium solution. This answers a question which...

urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. the main objective of this paper is to solve the urysohn type fredholm integral equation. to do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known legendre polynomials instead of the known function. after discretization of the problem o...

Abstract In this paper, we study the fractional nonlinear Rayleigh–Stokes equation under nonlocal integral conditions, and existence uniqueness of mild solution to our problem are considered. The ill-posedness recovering initial value is also investigated. To tackle ill-posedness, a regularized constructed by Fourier truncation method, convergence rate exact method demonstrated.

A unified treatment is given of low-weight modular forms on Γ0(N), N = 2, 3, 4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, from which a single nonlinear third-order equation, called a generalized Chazy equation, can be derived. As byproducts of this result, a table of divisor function...