On the generalized fractional snap boundary problems via G-Caputo operators: existence and stability analysis

This research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the $\mathbb{G}$ G -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional $\mathbb{G}$ G -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders.

Existence of quasi-periodic responses in quasi-periodically forced nonlinear mechanical systems

Forced responses of mechanical systems are crucial design and performance criteria. Hence, their robust and reliable calculation is of vital importance. While numerical computation of periodic responses benefits from an extensive mathematical basis, the literature for quasi-periodically forced systems is limited. More specifically, the absence of applicable and general existence criterion for quasi-periodic orbits of nonlinear mechanical systems impedes definitive conclusions from numerical methods such as harmonic balance. In this work, we establish a general existence criterion for quasi-periodically forced vibratory systems with nonlinear stiffness terms. Our criterion does not rely on any small parameters and hence is applicable for large response and forcing amplitudes. On explicit numerical examples, we demonstrate how our existence criterion can be utilized to justify subsequent numerical computations of forced responses.

R-Regularity of Set-Valued Mappings Under the Relaxed Constant Positive Linear Dependence Constraint Qualification with Applications to Parametric and Bilevel Optimization

The presence of Lipschitzian properties for solution mappings associated with nonlinear parametric optimization problems is desirable in the context of, e.g., stability analysis or bilevel optimization. An example of such a Lipschitzian property for set-valued mappings, whose graph is the solution set of a system of nonlinear inequalities and equations, is R-regularity. Based on the so-called relaxed constant positive linear dependence constraint qualification, we provide a criterion ensuring the presence of the R-regularity property. In this regard, our analysis generalizes earlier results of that type which exploited the stronger Mangasarian–Fromovitz or constant rank constraint qualification. Afterwards, we apply our findings in order to derive new sufficient conditions which guarantee the presence of R-regularity for solution mappings in parametric optimization. Finally, our results are used to derive an existence criterion for solutions in pessimistic bilevel optimization and a sufficient condition for the presence of the so-called partial calmness property in optimistic bilevel optimization.

Information Flow in Logics in the Vicinity of BB

Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised ver- sion of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB+(^I), which falls between Lavers' system BB+ and B+ , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions).

A search for c-Wieferich primes

Let [Formula: see text] be a power of a prime number [Formula: see text], [Formula: see text] be a finite field with [Formula: see text] elements and [Formula: see text] be a subgroup of [Formula: see text] of order [Formula: see text]. We give an existence criterion and an algorithm for computing maximally [Formula: see text]-fixed c-Wieferich primes in [Formula: see text]. Using the criterion, we study how c-Wieferich primes behave in [Formula: see text] extensions.

Approximate solutions for a fractional hybrid initial value problem via the Caputo conformable derivative

Our main purpose in this work is to derive an existence criterion for a Caputo conformable hybrid multi-term integro-differential equation equipped with initial conditions. In this way, we consider a partially ordered Banach space, and, by applying the lower solution property, the existence and successive approximations of solutions for the mentioned hybrid initial problem are investigated. Eventually, we formulate an illustrative example for this hybrid IVP to support our findings from a numerical point of view. Moreover, we plot the sequence of the obtained approximate solutions for different values of noninteger orders.

A mathematical analysis of a system of Caputo–Fabrizio fractional differential equations for the anthrax disease model in animals

We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional $\mathcal {CF}$ CF -system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number $\mathcal{R}_{0}$ R 0 of the fractional $\mathcal{CF}$ CF -system we compute two disease-free and endemic equilibrium points and check the asymptotic stability property. Moreover, by applying an iterative approach based on the Sumudu transform we investigate the stability of the fractional $\mathcal{CF}$ CF -system. We obtain approximate series solutions of this system by means of the homotopy analysis transform method, in which we invoke the linear Laplace transform. Finally, after the convergence analysis of the numerical method HATM, we present a numerical simulation of the $\mathcal{CF}$ CF -fractional anthrax disease model and review the dynamical behavior of the solutions of this $\mathcal {CF}$ CF -system during a time interval.