On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions
In this paper we study single-valued and multi-valued (<i>k</i>,<i>ψ</i>)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (<i>k</i>,<i>ψ</i>)-Hilfer-type derivative and integral operat...
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MDPI AG
2022-08-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/8/403 |
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| author | Sotiris K. Ntouyas Bashir Ahmad Cholticha Nuchpong Jessada Tariboon |
| author_facet | Sotiris K. Ntouyas Bashir Ahmad Cholticha Nuchpong Jessada Tariboon |
| author_sort | Sotiris K. Ntouyas |
| collection | DOAJ |
| description | In this paper we study single-valued and multi-valued (<i>k</i>,<i>ψ</i>)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (<i>k</i>,<i>ψ</i>)-Hilfer-type derivative and integral operators. The results for single-valued case are established by using Banach and Krasnosel’skiĭ fixed point theorems as well as Leray–Schauder nonlinear alternative. In the multi-valued case, we establish an existence result for the convex valued right-hand side of the inclusion via Leray–Schauder nonlinear alternative for multi-valued maps, while the second one when the right-hand side has non-convex values is obtained by applying Covitz–Nadler fixed point theorem for multi-valued contractions. Numerical examples illustrating the obtained theoretical results are also presented. |
| first_indexed | 2024-03-09T04:40:52Z |
| format | Article |
| id | doaj.art-4c356df4bccd40ecbf291c6e73906254 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T04:40:52Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-4c356df4bccd40ecbf291c6e739062542023-12-03T13:20:08ZengMDPI AGAxioms2075-16802022-08-0111840310.3390/axioms11080403On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary ConditionsSotiris K. Ntouyas0Bashir Ahmad1Cholticha Nuchpong2Jessada Tariboon3Department of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaThai-German Pre-Engineering School, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandIntelligent 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 study single-valued and multi-valued (<i>k</i>,<i>ψ</i>)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (<i>k</i>,<i>ψ</i>)-Hilfer-type derivative and integral operators. The results for single-valued case are established by using Banach and Krasnosel’skiĭ fixed point theorems as well as Leray–Schauder nonlinear alternative. In the multi-valued case, we establish an existence result for the convex valued right-hand side of the inclusion via Leray–Schauder nonlinear alternative for multi-valued maps, while the second one when the right-hand side has non-convex values is obtained by applying Covitz–Nadler fixed point theorem for multi-valued contractions. Numerical examples illustrating the obtained theoretical results are also presented.https://www.mdpi.com/2075-1680/11/8/403(<i>k</i>,<i>ψ</i>)-Hilfer fractional derivativeRiemann–Liouville fractional derivativeCaputo fractional derivativeexistenceuniquenessfixed point theorems |
| spellingShingle | Sotiris K. Ntouyas Bashir Ahmad Cholticha Nuchpong Jessada Tariboon On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions Axioms (<i>k</i>,<i>ψ</i>)-Hilfer fractional derivative Riemann–Liouville fractional derivative Caputo fractional derivative existence uniqueness fixed point theorems |
| title | On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions |
| title_full | On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions |
| title_fullStr | On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions |
| title_full_unstemmed | On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions |
| title_short | On (<i>k</i>,<i>ψ</i>)-Hilfer Fractional Differential Equations and Inclusions with Mixed (<i>k</i>,<i>ψ</i>)-Derivative and Integral Boundary Conditions |
| title_sort | on i k i i ψ i hilfer fractional differential equations and inclusions with mixed i k i i ψ i derivative and integral boundary conditions |
| topic | (<i>k</i>,<i>ψ</i>)-Hilfer fractional derivative Riemann–Liouville fractional derivative Caputo fractional derivative existence uniqueness fixed point theorems |
| url | https://www.mdpi.com/2075-1680/11/8/403 |
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