Special Functions as Solutions to the Euler–Poisson–Darboux Equation with a Fractional Power of the Bessel Operator

In this paper, we consider fractional ordinary differential equations and the fractional Euler–Poisson–Darboux equation with fractional derivatives in the form of a power of the Bessel differential operator. Using the technique of the Meijer integral transform and its modification, fundamental solutions to these equations are derived in terms of the Fox–Wright function, the Fox H-function, and their particular cases. We also provide some explicit formulas for the solutions to the corresponding initial-value problems in terms of the generalized convolutions introduced in this paper.

Symmetry Group for Solving Elliptic Euler-Poisson-Darboux Equation

The aim of this article is to study the solution of Elliptic Euler-Poisson-Darboux equation, by using the symmetry of Lie Algebra of orders two and three, as a contribution in partial differential equations and their solutions.

H∞ control for a class of two-dimensional linear systems with fading measurements

In this paper, the [Formula: see text] control problem for a class of two-dimensional (2-D) linear discrete-time systems with fading measurements is investigated, where the 2-D systems are described by a Roesser model. The Rice fading model is applied to describe the fading phenomenon and the coefficients of the model satisfy the independent identical Gaussian distributions. The main objective of this paper is to design a controller such that both the 2-D closed-loop system is exponentially mean-square stable and the prescribed [Formula: see text] performance is guaranteed under the condition of applying the attenuation signals. By utilizing the Lyapunov stability theory and the linear matrix inequalities (LMIs) techniques, sufficient conditions are conducted to guarantee the desired tracking performance. Based on such conditions, the gain matrix of the proposed controller is obtained. Finally, the effectiveness of the proposed control schemes is illustrated with a numerical example and a Darboux equation example.