AbstractThe fundamental goal of the study under consideration is to establish some of the existence criteria needed for a particular fractional inclusion model of cantilever beam in the setting of quantum calculus using new arguments of existence theory. In this way, we investigate a fractional integral equation that corresponds to the aforementioned boundary value problem. In a more concrete sense, we design new multi-valued operators based on this integral equation, which belong to the certain subclasses of functions, called α-admissible and α-ψ-contractive multi-functions, in combination with the AEP-property. Also, we use some inequalities such as Ω-inequality and set-valued version inequalities. Moreover, we add a simulative example for a numerical analysis of our results obtained in this study.
We consider the nonlinear n-th order boundary value problem Lu=u(n)=f(t,u(t),u′(t),…,u(n−1)(t))=Nu given arbitrary bounded linear functional conditions Bi(u)=0, i=1,…,n and develop a method that allows us to study all such resonance problems of order one, as well as implementing a more general constructive method for deriving existence criteria in the framework of the coincidence degree method of Mawhin. We demonstrate applicability of the formalism by giving an example for n=4.
This work recovers cubic–quartic soliton solutions to the Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also retrieved and enumerated. The existence criteria for the displayed solitons are also presented.
AbstractThe 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.
AbstractIn the existing study, we investigate the criteria of existence of solution for relatively new categories of φ-Caputo fractional differential equations and inclusions problems equipped with nonlocal φ-integral boundary conditions. In order to achieve the desired goal, we use α–ψ-contractive mappings and the theory of approximate endpoint. In the final stage, we exhibit some examples to provide the illustrations of our theoretical findings.
In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.
In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.
Abstract
The optical solitons in Bragg gratings fibers for perturbed NLSE having cubic-quartic dispersive reflectivity with parabolic-nonlocal combo law of refractive index are studied. The extended auxiliary equation method and the addendum to Kudryashov's method are introduced. The existence criteria for such solitons are indicated.
GStudied in this work are embedded solitons with quadratic nonlinearity that includes the effect of spatio-temporal dispersion. Two integration schemes yield bright, dark, singular and combo singular soliton solutions from the continuous regime. The existence criteria for these solitons are also included.
In this paper, a new class of a neutral functional delay differential equation involving the generalized
ψ
-Caputo derivative is investigated on a partially ordered Banach space. The existence and uniqueness results to the given boundary value problem are established with the help of the Dhage’s technique and Banach contraction principle. Also, we prove other existence criteria by means of the topological degree method. Finally, Ulam-Hyers type stability and its generalized version are studied. Two illustrative examples are presented to demonstrate the validity of our obtained results.
On a fractional cantilever beam model in the q-difference inclusion settings via special multi-valued operators
