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The Special Issue contains eleven accepted and published submissions to a Special Issue of the MDPI journal Axioms on the subject of “Nonlinear Dynamical Systems with Applications” [...]

During the last years several fractional integrals were investigated. Having this idea in mind, in the present article, some new generalized fractional integral inequalities of the trapezoidal type for λφ–preinvex functions, which are differentiable and twice differentiable, are established. Then, by employing those results, we explore the new estimates on trapezoidal type inequalities for classical integral and Riemann–Liouville fractional integrals, respectively. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable.

The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.

In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hemivariational inequalities involving history-dependent operators and related problems with periodic and antiperiodic boundary conditions. The applicability of our theoretical results is illustrated through applications to a fractional evolution inclusion and a dynamic semipermeability problem.

In this paper, some novel conditions for the stability results for a class of fractional-order quasi-linear impulsive integro-differential systems with multiple delays is discussed. First, the existence and uniqueness of mild solutions for the considered system is discussed using contraction mapping theorem. Then, novel conditions for Mittag–Leffler stability (MLS) of the considered system are established by using well known mathematical techniques, and further, the two corollaries are deduced, which still gives some new results. Finally, an example is given to illustrate the applications of the results.

In this paper, we study a class of generalized and not necessarily differentiable functionals of the form J(u) =∫ΩG(x,∇u)dx −∫Ωj1(x,u)dx −∫∂Ωj2(x,u)dσ with functions j1: Ω × ℝ → ℝ, j2: ∂Ω × ℝ → ℝ that are only locally Lipschitz in the second argument and involving critical growth for the elements of their generalized gradients ∂jk(x,⋅),k = 1, 2 even on the boundary ∂Ω. We generalize the famous result of Brezis and Nirenberg [H1 versus C1 local minimizers, C. R. Acad. Sci. Paris Sér. I Math. 317(5) (1993) 465–472] to a more general class of functionals and extend all the other generalizations of this result which has been published in the last decades.

Fractional integral inequality plays a significant role in pure and applied mathematics fields. It aims to develop and extend various mathematical methods. Therefore, nowadays we need to seek accurate fractional integral inequalities in obtaining the existence and uniqueness of the fractional methods. Besides, the convexity theory plays a concrete role in the field of fractional integral inequalities due to the behavior of its definition and properties. There is also a strong relationship between convexity and symmetric theories. So, whichever one we work on, we can then apply it to the other one due to the strong correlation produced between them, specifically in the last few decades. First, we recall the definition of φ-Riemann–Liouville fractional integral operators and the recently defined class of convex functions, namely the σ˘-convex functions. Based on these, we will obtain few integral inequalities of Hermite–Hadamard’s type for a σ˘-convex function with respect to an increasing function involving the φ-Riemann–Liouville fractional integral operator. We can conclude that all derived inequalities in our study generalize numerous well-known inequalities involving both classical and Riemann–Liouville fractional integral inequalities. Finally, application to certain special functions are pointed out.

In this paper, we introduce and study a fractional elliptic obstacle system, which is composed of two elliptic inclusions with fractional (pi; qi)-Laplace operators, nonlocal functions, and multivalued terms. The weak solution of fractional elliptic obstacle system is formulated by a fully nonlinear coupled system driven by two nonlinear and nonmonotone variational inequalities with constraints. The nonemptiness and compactness of solution set in the weak sense are proved via employing a surjectivity theorem to the multivalued operators formulated by the sum of a multivalued pseudomonotone operator and a maximal monotone operator. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the stability analysis for a contaminant convection-reaction-diffusion model of the recovered fracturing fluid (RFFM, for short), which couples a nonlinear and non-smooth stationary incompressible Navier-Stokes equation with a multivalued frictional boundary condition, and a nonlinear reaction-diffusion equation with mixed Neumann boundary conditions. First, we introduce a family of perturbation problems corresponding to (RFFM), and present the variational formulation of perturbation problem which is a perturbation elliptic hemivariational inequality driven by a perturbation nonlinear variational equation. Then, the existence of solutions and the uniform bound of the solution set to the perturbation problem are obtained. Finally, it is established that, as the perturbation parameter tends to zero, the solution set of the perturbation problems converge to the solution set of (RFFM) in the sense of the Kuratowski upper limit. This shows that (RFFM) is stable with respect to the perturbation data. [ABSTRACT FROM AUTHOR]