Existence Results for ψ -Hilfer Fractional Integro-Differential Hybrid Boundary Value Problems for Differential Equations and Inclusions

In this research work, we study a new class of ψ -Hilfer hybrid fractional integro-differential boundary value problems with nonlocal boundary conditions. Existence results are established for single and multivalued cases, by using suitable fixed-point theorems for the product of two single or multivalued operators. Examples illustrating the main results are also constructed.

Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus

The key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital α-admissible and α-ψ-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.

Fixed Point, Data Dependence, and Well-Posed Problems for Multivalued Nonlinear Contractions

The aim of the paper is to discuss data dependence, existence of fixed points, strict fixed points, and well posedness of some multivalued generalized contractions in the setting of complete metric spaces. Using auxiliary functions, we introduce Wardowski type multivalued nonlinear operators that satisfy a novel class of contractive requirements. Furthermore, the existence and data dependence findings for these multivalued operators are obtained. A nontrivial example is also provided to support the results. The results generalize, improve, and extend existing results in the literature.

Formulation and existence of weak solutions for a problem of adhesive contact with elastoplasticity and hardening

This paper presents the weak formulation of a quasi-static evolution model for two deformable bodies with uni-directional adhesive unilateral contact on which external loads act. Small deformations and linearized elastoplasticity with hardening are assumed. The adhesion component is rate-dependent or rate-independent according to the choice of the viscosity coefficient of the glue; elastoplasticity is considered rate-independent. The weak formulation is expressed as a doubly non-linear problem with unbounded multivalued operators, as a function of internal and boundary displacements, plastic and symmetric strain tensors, and the bonding field and its gradient. This paper differs from other formulations by coupling the equations defined inside and on the boundary of the solids in functional form. In addition to this novelty, we verify the existence of solutions by a path other than that displayed in similar articles. The existence of solutions is demonstrated after considering a succession of doubly non-linear problems with an unbounded operator, and verifying that the solution of one of the problems is also a solution to the objective problem. The proof is supported by previous results from non-linear Partial differential equations theory with monotone operators.

Frum-Ketkov type multivalued operators

Let (M,d) be a metric space, X\subset M be a nonempty closed subset and K\subset M be a nonempty compact subset. By definition, an upper semi-continuous multivalued operator F:X\to P(X) is said to be a strong Frum-Ketkov type operator if there exists \alpha\in ]0,1[ such that e_d(F(x),K)\le \alpha D_d(x,K), for every x\in X, where e_d is the excess functional generated by d and D_d is the distance from a point to a set. In this paper, we will study the fixed points of strong Frum-Ketkov type multivalued operators.

Existence results for double phase implicit obstacle problems involving multivalued operators

In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.

A new approach to multivalued nonlinear weakly Picard operators

The notion of nonlinear $(\mathcal{F}_{s}, \mathcal{L})$(Fs,L)-contractive multivalued operators is initiated and some related fixed point results are considered. We also give an example to show the validity of obtained theoretical results. Our results generalize many existing ones in the literature.

Characterization of a b-metric space completeness via the existence of a fixed point of Ciric-Suzuki type quasi-contractive multivalued operators and applications

The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved.