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Search Results (4)

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Keywords = anti-periodic boundary value problem

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15 pages, 331 KiB  
Article
Existence and Uniqueness Results for Different Orders Coupled System of Fractional Integro-Differential Equations with Anti-Periodic Nonlocal Integral Boundary Conditions
by Ymnah Alruwaily, Shorog Aljoudi, Lamya Almaghamsi, Abdellatif Ben Makhlouf and Najla Alghamdi
Symmetry 2023, 15(1), 182; https://doi.org/10.3390/sym15010182 - 7 Jan 2023
Cited by 7 | Viewed by 2017
Abstract
This paper presents a new class of boundary value problems of integrodifferential fractional equations of different order equipped with coupled anti-periodic and nonlocal integral boundary conditions. We prove the existence and uniqueness criteria of the solutions by using the Leray-Schauder alternative and Banach [...] Read more.
This paper presents a new class of boundary value problems of integrodifferential fractional equations of different order equipped with coupled anti-periodic and nonlocal integral boundary conditions. We prove the existence and uniqueness criteria of the solutions by using the Leray-Schauder alternative and Banach contraction mapping principle. Examples are constructed for the illustration of our results. Full article
(This article belongs to the Special Issue Applied Mathematics and Fractional Calculus II)
16 pages, 316 KiB  
Article
Fractional-Order Integro-Differential Multivalued Problems with Fixed and Nonlocal Anti-Periodic Boundary Conditions
by Ahmed Alsaedi, Ravi P. Agarwal, Sotiris K. Ntouyas and Bashir Ahmad
Mathematics 2020, 8(10), 1774; https://doi.org/10.3390/math8101774 - 14 Oct 2020
Cited by 2 | Viewed by 1871
Abstract
This paper studies a new class of fractional differential inclusions involving two Caputo fractional derivatives of different orders and a Riemann–Liouville type integral nonlinearity, supplemented with a combination of fixed and nonlocal (dual) anti-periodic boundary conditions. The existence results for the given problem [...] Read more.
This paper studies a new class of fractional differential inclusions involving two Caputo fractional derivatives of different orders and a Riemann–Liouville type integral nonlinearity, supplemented with a combination of fixed and nonlocal (dual) anti-periodic boundary conditions. The existence results for the given problem are obtained for convex and non-convex cases of the multi-valued map by applying the standard tools of the fixed point theory. Examples illustrating the obtained results are presented. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)
15 pages, 291 KiB  
Article
Existence of Solutions for Anti-Periodic Fractional Differential Inclusions Involving ψ-Riesz-Caputo Fractional Derivative
by Dandan Yang and Chuanzhi Bai
Mathematics 2019, 7(7), 630; https://doi.org/10.3390/math7070630 - 15 Jul 2019
Cited by 6 | Viewed by 2917
Abstract
In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear [...] Read more.
In this paper, we investigate the existence of solutions for a class of anti-periodic fractional differential inclusions with ψ -Riesz-Caputo fractional derivative. A new definition of ψ -Riesz-Caputo fractional derivative of order α is proposed. By means of Contractive map theorem and nonlinear alternative for Kakutani maps, sufficient conditions for the existence of solutions to the fractional differential inclusions are given. We present two examples to illustrate our main results. Full article
(This article belongs to the Special Issue Fractional Differential Equations, Inclusions and Inequalities with Applications)
15 pages, 296 KiB  
Article
Anti-Periodic Boundary Value Problems for Nonlinear Langevin Fractional Differential Equations
by Fang Li, Hongjuan Zeng and Huiwen Wang
Symmetry 2019, 11(4), 443; https://doi.org/10.3390/sym11040443 - 27 Mar 2019
Cited by 2 | Viewed by 2570
Abstract
In this paper, we focus on the existence of solutions of the nonlinear Langevin fractional differential equations involving anti-periodic boundary value conditions. By using some techniques, formulas of solutions for the above problem and some properties of the Mittag-Leffler functions [...] Read more.
In this paper, we focus on the existence of solutions of the nonlinear Langevin fractional differential equations involving anti-periodic boundary value conditions. By using some techniques, formulas of solutions for the above problem and some properties of the Mittag-Leffler functions E α , β ( z ) , α , β ∈ ( 1 , 2 ) , z ∈ R are presented. Moreover, we utilize the fixed point theorem under the weak assumptions for nonlinear terms to obtain the existence result of solutions and give an example to illustrate the result. Full article
(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)
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