We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0 D t u+ ∑d i=1 [cli aiD 2μi xi u+cri xiD 2μi bi u]+γ u = ∑d j=1 [κl j a jD 2ν j x j u+κr j x jD 2ν j b j u]+ f , where 2τ ∈ (0, 2), 2μi ∈ (0, 1) and 2ν j ∈ (1, 2), in a (1+d)-dimensional space-time hypercube, d = 1, 2, 3,...

Abstract We prove local solvability and stability of the inverse Robin–Regge problem in general case, taking eigenvalue multiplicities into account. develop new approach based on reduction this to recovery Sturm–Liouville potential from Cauchy data

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form 0D t u+ ∑d i=1[cli aiD 2μi xi u+ cri xiD 2μi bi u] +γ u = ∑d j=1[ κlj ajD 2νj xj u+κrj xjD 2νj bj u] +f , where 2τ ∈ (0, 2), 2μj ∈ (0, 1) and 2νj ∈ (1, 2), in a (1 +d)-dimensional space-time hypercube, d = 1, 2, 3, · · · ,...

In this paper, we consider the inverse problem for Sturm-Liouville operators with eigenparameter dependent boundary conditions on time scales. We give new uniqueness theorems and investigate its some special cases.