Related papers: Inverse Nodal Problem for a Conformable Fractional…
A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…
This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
In this work, the Dirac-type integro di{\S}erential system with one classical boundary condition and another nonlocal integral boundary condition is considered. We obtain the asymptotic formulae for the solutions, eigenvalues and nodal…
Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonlinear terms in the semilinear equations from the knowledge of…
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…
We prove that conformable ``fractional" differentiability of a function $f:[0,\infty[\,\longrightarrow \mathbb{R}$ is nothing else than the classical differentiability. More precisely, the conformable $\alpha$-derivative of $f$ at some…
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…
In this paper, we are interested in an inverse problem for the active scalar equations with fractional dissipation on the torus. We perform a second order linearization to relate our model to the linear fractional diffusion equation. Our…
In this study, we investigate the traces and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with retarded argument and with a finite number of transmission conditions.
In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.
Nowadays, fractional differential equations are a well established tool to model phenomena from the real world. Since the analytical solution is rarely available, there is a great effort in constructing efficient numerical methods for their…
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 consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
The initial inverse problem of finding solutions and their initial values ($t = 0$) appearing in a general class of fractional reaction-diffusion equations from the knowledge of solutions at the final time ($t = T$). Our work focuses on the…
In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
We study the inverse problem of recovering a semilinear diffusion term $a(t,\lambda)$ as well as a quasilinear convection term $\mathcal B(t,x,\lambda,\xi)$ in a nonlinear parabolic equation $$\partial_tu-\textrm{div}(a(t,u) \nabla…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…