We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-infinite cylinder in one more spatial dimension. We write our evolution ...

Our work concerns the study of inverse problems heat and wave equations involving fractional Laplacian operator with zeroth order nonlinear perturbations. We recover terms in semilinear from knowledge Dirichlet-to-Neumann type map combined Runge approximation unique continuation property Laplacian.

Application of fractional calculus to the description of anomalous diffusion and relaxation processes in complex media provided one of the most impressive impulses to the development of statistical physics during the last decade. In particular the so-called fractional diffusion equation enabled one to capture the main features of anomalous diffusion. However the price for this achievement is ra...

This paper considers the attenuated Westervelt equation in pressure formulation. The attenuation is by various models proposed literature and characterised inclusion of non-local operators that give power law damping as opposed to exponential classical models. goal inverse problem recovering a spatially dependent coefficient equation, parameter nonlinearity <inline-formula content-type="math/ma...

 Abstract: Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the Least-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the ...

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...