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Results reported in this paper establish the existence of solutions for a class of generalized fractional inclusions based on the Caputo–Hadamard jerk system. Under some inequalities between multi-functions and with the help of special contractions and admissible maps, we investigate the existence criteria. Fixed points and end points are key roles in this manuscript, and the approximate property for end points helps us to derive the desired result for existence theory. An example is prepared to demonstrate the consistency and correctness of analytical findings. [ABSTRACT FROM AUTHOR]

The 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. [ABSTRACT FROM AUTHOR]

In this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville–Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski's measure of noncompactness and Sadovskii's fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the existence and uniqueness of solutions for a new neutral hybrid nonlinear differential equation in the context of a fractional generalized operator in the sense of ψ-Caputo. To emphasize the novelty of the manuscript, a pure technique of the noncompactness measures is applied to a hybrid system based on the notion of the modulus of continuity in Darbo's criterion that covers the existing results of other works published before. The Ulam–Hyers and generalized Ulam–Hyers stabilities are explored for the given neutral nonhybrid nonlinear problem. An application is prepared in the framework of an example to ensure the validity of theorems for different cases. [ABSTRACT FROM AUTHOR]

In this paper, we study a new class of non-hybrid single-valued fractional boundary value problems equipped with integro-non-hybrid-multiterm-multipoint-multistrip conditions and a fully hybrid integro-multi-valued fractional boundary value problem by some new methods including the Kuratowski measures based on Sadovskii's theorem, Krasnoselskii–Zabreiko criterion, and Dhage's technique. We generalize the Gronwall inequality in relation to a non-hybrid single-valued fractional boundary value problem, and then we investigate the stability notions in two versions. To examine the correctness of the results, we provide some examples. [ABSTRACT FROM AUTHOR]