In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

In this study, we establish a Parseval equality and an expansion formula for a Sturm– Liouville operator on semi-unbounded time scales. AMS subject classification: 34L10.

We solve the inverse spectral problem for a class of Sturm–Liouville operators with singular nonlocal potentials and nonlocal boundary conditions.

‎it is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎for‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎this paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎the fractional derivatives are described...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

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...

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm–Liouville and Dirac operators by the eigenvalues of regular operators.