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Search Results (4)

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Keywords = Caputo fractional (p, q)-difference equations

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18 pages, 338 KiB  
Article
Existence of Solutions for Caputo-Type Fractional (p,q)-Difference Equations Under Robin Boundary Conditions
by Hailong Ma and Hongyu Li
Axioms 2025, 14(4), 318; https://doi.org/10.3390/axioms14040318 - 21 Apr 2025
Viewed by 405
Abstract
In this paper, we investigate the existence results of solutions for Caputo-type fractional (p,q)-difference equations. Using Banach’s fixed-point theorem, we obtain the existence and uniqueness results. Meanwhile, by applying Krasnoselskii’s fixed-point theorem and Leray-Schauder’s nonlinear alternative, we also [...] Read more.
In this paper, we investigate the existence results of solutions for Caputo-type fractional (p,q)-difference equations. Using Banach’s fixed-point theorem, we obtain the existence and uniqueness results. Meanwhile, by applying Krasnoselskii’s fixed-point theorem and Leray-Schauder’s nonlinear alternative, we also obtain the existence results of non-trivial solutions. Finally, we provide examples to verify the correctness of the given results. Moreover, relevant applications are presented through specific examples. Full article
(This article belongs to the Special Issue Fractional Calculus—Theory and Applications, 3rd Edition)
29 pages, 464 KiB  
Article
On Solutions of Two Post-Quantum Fractional Generalized Sequential Navier Problems: An Application on the Elastic Beam
by Sina Etemad, Sotiris K. Ntouyas, Ivanka Stamova and Jessada Tariboon
Fractal Fract. 2024, 8(4), 236; https://doi.org/10.3390/fractalfract8040236 - 17 Apr 2024
Cited by 9 | Viewed by 1629
Abstract
Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, [...] Read more.
Fractional calculus provides some fractional operators for us to model different real-world phenomena mathematically. One of these important study fields is the mathematical model of the elastic beam changes. More precisely, in this paper, based on the behavior patterns of an elastic beam, we consider the generalized sequential boundary value problems of the Navier difference equations by using the post-quantum fractional derivatives of the Caputo-like type. We discuss on the existence theory for solutions of the mentioned (p;q)-difference Navier problems in two single-valued and set-valued versions. We use the main properties of the (p;q)-operators in this regard. Application of the fixed points of the ρ-θ-contractions along with the endpoints of the multi-valued functions play a fundamental role to prove the existence results. Finally in two examples, we validate our models and theoretical results by giving numerical models of the generalized sequential (p;q)-difference Navier problems. Full article
(This article belongs to the Special Issue Advances in Boundary Value Problems for Fractional Differential Equations, 2nd Edition)
15 pages, 818 KiB  
Article
Existence and Uniqueness Results for Fractional (p, q)-Difference Equations with Separated Boundary Conditions
by Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas and Bashir Ahmad
Mathematics 2022, 10(5), 767; https://doi.org/10.3390/math10050767 - 28 Feb 2022
Cited by 10 | Viewed by 2516
Abstract
In this paper, we study the existence of solutions to a fractional (p, q)-difference equation equipped with separate local boundary value conditions. The uniqueness of solutions is established by means of Banach’s contraction mapping principle, while the existence [...] Read more.
In this paper, we study the existence of solutions to a fractional (p, q)-difference equation equipped with separate local boundary value conditions. The uniqueness of solutions is established by means of Banach’s contraction mapping principle, while the existence results of solutions are obtained by applying Krasnoselskii’s fixed-point theorem and the Leary–Schauder alternative. Some examples illustrating the main results are also presented. Full article
(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications II)
20 pages, 865 KiB  
Article
Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations
by Pheak Neang, Kamsing Nonlaopon, Jessada Tariboon, Sotiris K. Ntouyas and Bashir Ahmad
Fractal Fract. 2021, 5(4), 270; https://doi.org/10.3390/fractalfract5040270 - 10 Dec 2021
Cited by 12 | Viewed by 2910
Abstract
In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness [...] Read more.
In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented. Full article
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