In this paper, in the cylindrical domain, we consider a fractional elliptic operator with Dirichlet conditions. We prove, that first eigenvalue of is minimised circular cylinder among all domains same Lebesgue measure. This inequality called Rayleigh–Faber–Krahn inequality. Also, give Lyapunov and Hartmann–Wintner inequalities for boundary value problem.

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, apply Schaefer’s fixed point theorem. Furthermore, present Lyapunov inequality for corresponding problem.

In this paper, an impulsive conformable fractional Lotka–Volterra model with dispersion is introduced. Since the concept of derivatives avoids some limitations classical fractional-order derivatives, it more suitable for applied problems. The control approach which common population dynamics’ models and fixed moments perturbations are considered. combined practical stability respect to manifold...

In this paper, we study the recently proposed fractional-order operators with general analytic kernels. The kernel of these is a locally uniformly convergent power series that can be chosen adequately to obtain family fractional and, in particular, main existing derivatives. Based on conditions for Laplace transform operators, some new results are obtained—for example, relationships between Rie...

In this study, two lagged fractional order singular neutral differential equations are considered. Using the advantage of association property Riemann -Liouville derivative, derivative appropriate Lyapunov function is calculated. Then, with help LMI, sufficient conditions for asymptotic stability zero solutions obtained.

A system of nonlinear fractional differential equations with the Riemann–Liouville derivative is considered. Lipschitz stability in time for studied defined and studied. This connected singularity at initial point. Two types derivatives Lyapunov functions among are applied to obtain sufficient conditions property. Some examples illustrate results.

This paper emphasized on studying the asymptotic synchronization and finite of fractional-order memristor-based inertial neural networks with time-varying latency. The network model is offered as a more general flexible alternative to integer-order network. By utilizing properties fractional calculus, two lemmas stability finite-time are provided. Based constructed Lyapunov functionals, some up...

This paper establishes Lyapunov-type inequalities for a family of two-point $(\mathtt{n},\mathtt{p})$-type boundary value problems Riemann-Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide few examples, one which is equation with delay.

This paper investigates set-valued differential equations with fractional-like Hukuhara derivatives. Firstly, a novel comparison principle is given by introducing the upper quasi-monotone increasing functions. Then, stability criteria of Lipschitz and practical such different initial time are obtained via new vector Lyapunov