In this paper, we would like to briefly introduce some applications of fractional derivatives in the fields heat and fluid-flows. However, our main focus is on study an inverse source problem for Rayleigh-Stokes problem. The severely ill-posed. We verify ill-posedness Problem 1, applying modified Lavrentiev construct a regularization from exact data. After that, established convergent rate betw...

Recently, several works have been undertaken in an attempt to develop a theory for linear or sublinear elliptic equations involving general class of nonlocal operators characterized by mild assumptions on the associated Green kernel. In this paper, we study Dirichlet problem superlinear equation (E) $$\mathbb{L}u=u^{P}+\delta\mu$$ bounded domain Ω with homogeneous boundary exterior condition, w...