We study the inverse boundary value problem on determining a space-dependent component in right-hand side of semilinear time fractional diffusion-wave equation. find sufficient conditions for time-local uniqueness solution under time-integral additional condition \[\frac{1}{T}\int_{0}^{T}u(x,t)\eta_1(t)dt=\Phi_1(x), \;\;\;x\in \Omega\subset \Bbb R^n\] where $u$ is unknown first such equation, $...

The inverse tempered stable subordinator is a stochastic process that models power law waiting times between particle movements, with an exponential tempering that allows all moments to exist. This paper shows that the probability density function of an inverse tempered stable subordinator solves a tempered time-fractional diffusion equation, and its ‘‘folded’’ density solves a tempered time-fr...

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two mai...

<p style='text-indent:20px;'>We study the well-posedness of a semi-linear fractional diffusion equation and formulate an associated inverse problem. We determine power type nonlinearities from exterior partial measurements Dirichlet-to-Neumann map. Our arguments are based on first order linearization as well parabolic Runge approximation property.</p>

In this article, we deal with the inverse problem of identifying unknown source time-fractional diffusion equation in a cylinder by A fractional Landweber method. This is ill-posed. Therefore, regularization required. The main result article error between sought solution and its regularized under selection priori parameter choice rule.

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also pre...