Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions
In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the ex...
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MDPI AG
2021-07-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/174 |
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| author | Chanakarn Kiataramkul Weera Yukunthorn Sotiris K. Ntouyas Jessada Tariboon |
| author_facet | Chanakarn Kiataramkul Weera Yukunthorn Sotiris K. Ntouyas Jessada Tariboon |
| author_sort | Chanakarn Kiataramkul |
| collection | DOAJ |
| description | In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented. |
| first_indexed | 2024-03-10T07:54:16Z |
| format | Article |
| id | doaj.art-79c285996b934e5684ea7b9dd4823bce |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T07:54:16Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-79c285996b934e5684ea7b9dd4823bce2023-11-22T12:02:29ZengMDPI AGAxioms2075-16802021-07-0110317410.3390/axioms10030174Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary ConditionsChanakarn Kiataramkul0Weera Yukunthorn1Sotiris K. Ntouyas2Jessada Tariboon3Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandFaculty of Science and Technology, Kanchanaburi Rajabhat University, Kanchanaburi 71000, ThailandDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandIn this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.https://www.mdpi.com/2075-1680/10/3/174coupled systemsRiemann–Liouville fractional derivativeHadamard–Caputo fractional derivativenonlocal boundary conditionsexistencefixed point |
| spellingShingle | Chanakarn Kiataramkul Weera Yukunthorn Sotiris K. Ntouyas Jessada Tariboon Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions Axioms coupled systems Riemann–Liouville fractional derivative Hadamard–Caputo fractional derivative nonlocal boundary conditions existence fixed point |
| title | Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions |
| title_full | Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions |
| title_fullStr | Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions |
| title_full_unstemmed | Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions |
| title_short | Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions |
| title_sort | sequential riemann liouville and hadamard caputo fractional differential systems with nonlocal coupled fractional integral boundary conditions |
| topic | coupled systems Riemann–Liouville fractional derivative Hadamard–Caputo fractional derivative nonlocal boundary conditions existence fixed point |
| url | https://www.mdpi.com/2075-1680/10/3/174 |
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