New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions
In this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions CDq+kCDq−1ut=ft,ut,CDq−1ut,t∈0,1,α1u0+β1u1+γ1Iruη=ε1,η∈0,1,α2u′0+β2u′1+γ2Iru′η=ε2, where q∈1,2 is a real number, k,r>0,αi,βi,γi,εi∈ℝ,i=1,2,CDq is the Caputo fractional derivative, and...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6821637 |
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| author | Haiyan Zhang Yaohong Li Jingbao Yang |
| author_facet | Haiyan Zhang Yaohong Li Jingbao Yang |
| author_sort | Haiyan Zhang |
| collection | DOAJ |
| description | In this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions CDq+kCDq−1ut=ft,ut,CDq−1ut,t∈0,1,α1u0+β1u1+γ1Iruη=ε1,η∈0,1,α2u′0+β2u′1+γ2Iru′η=ε2, where q∈1,2 is a real number, k,r>0,αi,βi,γi,εi∈ℝ,i=1,2,CDq is the Caputo fractional derivative, and the boundary conditions include antiperiodic and Riemann-Liouville fractional integral boundary value cases. Our approach to treat the above problem is based upon standard tools of fixed point theory and some new inequalities of norm form. Some existence results are obtained and well illustrated through the aid of examples. |
| format | Article |
| id | doaj-art-16a483a75ca44a80926448d2d28b375d |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-16a483a75ca44a80926448d2d28b375d2025-08-20T02:02:36ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/68216376821637New Sequential Fractional Differential Equations with Mixed-Type Boundary ConditionsHaiyan Zhang0Yaohong Li1Jingbao Yang2School of Mathematics and Statistics, Suzhou University, Suzhou, Anhui 234000, ChinaSchool of Mathematics and Statistics, Suzhou University, Suzhou, Anhui 234000, ChinaDepartment of Education, Bozhou University, Bozhou, Anhui 2368000, ChinaIn this paper, we introduce new sequential fractional differential equations with mixed-type boundary conditions CDq+kCDq−1ut=ft,ut,CDq−1ut,t∈0,1,α1u0+β1u1+γ1Iruη=ε1,η∈0,1,α2u′0+β2u′1+γ2Iru′η=ε2, where q∈1,2 is a real number, k,r>0,αi,βi,γi,εi∈ℝ,i=1,2,CDq is the Caputo fractional derivative, and the boundary conditions include antiperiodic and Riemann-Liouville fractional integral boundary value cases. Our approach to treat the above problem is based upon standard tools of fixed point theory and some new inequalities of norm form. Some existence results are obtained and well illustrated through the aid of examples.http://dx.doi.org/10.1155/2020/6821637 |
| spellingShingle | Haiyan Zhang Yaohong Li Jingbao Yang New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions Journal of Function Spaces |
| title | New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions |
| title_full | New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions |
| title_fullStr | New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions |
| title_full_unstemmed | New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions |
| title_short | New Sequential Fractional Differential Equations with Mixed-Type Boundary Conditions |
| title_sort | new sequential fractional differential equations with mixed type boundary conditions |
| url | http://dx.doi.org/10.1155/2020/6821637 |
| work_keys_str_mv | AT haiyanzhang newsequentialfractionaldifferentialequationswithmixedtypeboundaryconditions AT yaohongli newsequentialfractionaldifferentialequationswithmixedtypeboundaryconditions AT jingbaoyang newsequentialfractionaldifferentialequationswithmixedtypeboundaryconditions |