Abstract
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.
Highlights
With the passing of years and even decades, people need to be more and more aware of details of various natural phenomena
The following lemma presents a solution to the proposed problem (3) in the form of an integral equation, which is important in determining our key findings
A function μ belonging to CA∗ (O, A∗) is regarded as a solution of the sequential generalized q-Navier FBVP (4) if it fulfills the given BCs and there exists ∈ L1(O) such that (t) ∈ M(t, μ(t), CDq2 μ(t)) for almost all t ∈ O and μ(t) =
Summary
With the passing of years and even decades, people need to be more and more aware of details of various natural phenomena. The logical tools and notions available in mathematics and especially mathematical operators are one of possible ways to achieve this aim in modeling various processes. In this direction, many researchers developed numerous fractional operators such that their applicability and usefulness become more and more evident to researchers each day. As a result, using fractional operators, different processes are modeled and examined from all aspects in the mathematical structures such as boundary value problems In broad fields such as chemistry, biology, physics, economics, engineering, and so on fractional calculus, related differential equations and BVPs are commonly used [1,2,3,4,5]. In a vast domain of papers, scientists have examined numerous mathematical procedures across different facets of fractional differential equations [6,7,8,9,10,11,12,13]
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