For a spatially flat Friedmann model with line element ds 2 = a 2 [da 2 /B(a) − dx 2 − dy 2 − dz 2 ], the 00-component of the Einstein field equation reads 8πGT 00 = 3/a 2 containing no derivative. For a nonlinear Lagrangian L(R), we obtain a second– order differential equation for B instead of the expected fourth-order equation. We discuss this equation for the curvature-saturated model propos...

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

Properties of solutions of a bistable nonlinear convolution equation in higher space dimensions are studied. The nonlinearity is the derivative of a double well function. The theory of traveling waves for this equation was given in a previous publication 4]. Here we consider spreading phenomena for state regions, in some cases by means of the motion of domain walls, which are modeled by interna...

Properties of solutions of a bistable nonlinear convolution equation in higher space dimensions are studied. The nonlinearity is the derivative of a double well function. The theory of traveling waves for this equation was given in a previous publication [4]. Here we consider spreading phenomena for state regions, in some cases by means of the motion of domain walls, which are modeled by intern...

Existence of positive solutions for the nonlinear fractional differential equation Dsu(x) = f (x,u(x)), 0 < s < 1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804–812), where Ds denotes Riemann–Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential equation: L(D)u= f (x,u), u(0)= 0, 0 < x < 1...

In this paper, a general family of derivative-free n + 1-point iterative methods using 1 evaluations the function and n-point only one evaluation its derivative are constructed by inverse interpolation with memory on previous step for solving simple root nonlinear equation. The order convergence them proved respectively. Finally, proposed basins attraction demonstrated numerical examples.

In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse transform. Further, find solution nonlinear reaction diffusion equation with by applying Fourier transforms.

The existence of inertial manifolds for a Smoluchowski equation arising in the 2D Doi-Hess model for liquid crystalline polymers subjected to a shear flow is investigated. The presence of a non-variational drift term complicates the dynamics dramatically from the gradient case in which the it is characterized solely by the steady states. Several transformations are used in order to bring the eq...

In this paper, two significant inequalities for the Hilfer fractional derivative of a function in space ACγ([0,b],Rn), 0≤γ≤1 are obtained. We first verified extremum principle derivative. addition, we estimated at its extreme points. Furthermore, derived and proved maximum nonlinear differential equation. Finally, analyzed solutions Our results generalize extend some obtained theorems on topic.