In this paper, we study a coupled fully hybrid system of (k,Φ)–Hilfer fractional differential equations equipped with non-symmetric (k,Φ)–Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, use Krasnoselskii Perov fixed-point theorems Lipschitzian matrix in context generalized Banach space (GBS). Moreover, Ulam–Hyers (UH) stability solutions is discussed b...

We consider nonclassical entropy solutions to scalar conservation laws with concaveconvex flux functions, whose set of leftand right-hand admissible states ul, ur across undercompressive shocks is selected by a kinetic function ur = φ(ul). We introduce a new definition for the (generalized) strength of classical and nonclassical shocks, allowing us to propose a generalized notion of total varia...

Let H(d) be the space of complex hermitian matrices of size d×d and let H+(d) ⊂ H(d) be the cone of positive semidefinite matrices. A linear operator Φ : H(d1) → H(d2) is said to be positive if Φ[H+(d1)] ⊂ H+(d2). The concurrence C(Φ; ·) of a positive operator Φ : H(d1) → H(d2) is a real-valued function on the cone H+(d1), defined as the largest convex function which coincides with 2 q σ d2 2 (...

In this paper, we propose a generalization of Rényi divergence, and then we investigate its induced geometry. This generalization is given in terms of a φ-function, the same function that is used in the definition of non-parametric φ-families. The properties of φ-functions proved to be crucial in the generalization of Rényi divergence. Assuming appropriate conditions, we verify that the general...

Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space Φ× in a convenient Gelfand triplet Φ ⊆ H ⊆ Φ×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized bases of eigenfunctions in both frameworks direct integrals and Gelfand tripl...

This paper considers the robust stability of the interconnection of a linear timeinvariant differential nominal system and passive uncertainties in the behavioral framework. A generalized version of the well-known passivity theorem is formulated by using quadratic differential forms. Based on the generalized passivity theorem, it is proved that, if the nominal system is Φ-passive, the interconn...

We show that b ∈ BMO( n) if and only if the commutator [b, Iα] of the multiplication operator by b and the fractional integral operator Iα is bounded from generalized Morrey spaces Lp,φ( n) to Lq,φ q/p ( n), where φ is non-decreasing, and 1 < p < ∞, 0 < α < n and 1/q = 1/p− α/n.

Generalized sampling provides a general mechanism for recovering an unknown input function f(x) ∈ H from the samples of the responses of m linear shift-invariant systems sampled at 1/mth the reconstruction rate. The system can be designed to perform a projection of f(x) onto the reconstruction subspace V (φ) = span{φ(x− k)}k∈Z ; for example, the family of bandlimited signals with φ(x) = sinc(x)...