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There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schr\"odinger equations with subcritical exponent. For some smooth bounded domain $\Omega\subset \mathbf R^n$, our boundary condition is given…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…
In this paper, we give explicit estimates that insure the existence of solutions for first order partial differential operators on compact manifolds, using a viscosity method. In the linear case, an explicit integral formula can be found,…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
We discuss the existence and non-existence of non-negative, non-decreasing solutions of certain perturbed Hammerstein integral equations with derivative dependence. We present some applications to nonlinear, second order boundary value…
We study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional Laplacian: (-\Delta)^{\alpha/2}u=\lambda u^q+u^{\frac{N+\alpha}{N-\alpha}}, \quad…
To have an uniform estimate for the solutions of the scalar curvature equation perturbed by a non linear term, we give some minimal condition on the scalar curvature.
This paper is devoted to the study of the existence of positive solutions for a problem related to a higher order fractional differential equation involving a nonlinear term depending on a fractional differential operator,…
We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…
We consider a new fractional impulsive differential hemivariational inequality which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework.…
In present paper, we establish sufficient conditions for existence and stability of solutions for system of nonlinear implicit fractional differential equations. The main techniques are based on method of successive approximations. Finally,…
We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…
This paper focuses on controllability results of stochastic delay partial functional integro-differential equations perturbed by fractional Brownian motion. Sufficient conditions are established using the theory of resolvent operators…
The work deals with the studies of the existence of solutions of an integro-differential equation in the situation of the difference of the standard Laplacian and the bi-Laplacian in the diffusion term. The proof of the existence of…
For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of the operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the…
We consider an equation with drift and either critical or supercritical fractional diffusion. Under a regularity assumption for the vector field that is marginally stronger than what is required for Holder continuity of the solutions, we…