The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on the problem. An expression for the derivative of the n-th eigenvalue with respect to a given parameter: an endpoint, a boundary condition constant, a coefficient or weight function, is found.

The current study presents a comprehensive Lie symmetry analysis for the time-fractional Mikhailov–Novikov–Wang (MNW) system with Riemann–Liouville fractional derivative. corresponding simplified equations Erdélyi–Kober derivative are constructed by group invariant solutions. Furthermore, we obtain explicit solutions help of power series method and show dynamical behavior via evolutional figure...

We study the nonlocal boundary value problem for a mixed type equation with Riemann–Liouville fractional partial derivative. In hyperbolic part of domain, functional is solved by iteration method. The reduced to solving differential equation.

Using the reviewed Riemann-Liouville fractional derivative we define the bundle αk E = Osc(M) and highlight geometrical structures with a geometrical character. Also, we introduce the fractional osculator Lagrange space of k order and the main structures on it. The results are applied at the k order fractional prolongation of Lagrange, Finsler and Riemann fractional structures. Mathematics Subj...

In the present work we discuss the existence of solutions for a system of nonlinear fractional integro-differential equations with initial conditions. This system involving the Caputo fractional derivative and Riemann−Liouville fractional integral. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.