Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions
Boundary conditions involving fractional derivatives of unknown functions are more general and can be used to generalize Dirichlet- or Neumann-type boundary conditions. In this article, we consider a class of nonlinear fractional differential equations having Atangana-Baleanu derivatives equipped wi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-06-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823002454 |
| _version_ | 1827970964630011904 |
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| author | Kiran Kumar Saha N. Sukavanam Sonjoy Pan |
| author_facet | Kiran Kumar Saha N. Sukavanam Sonjoy Pan |
| author_sort | Kiran Kumar Saha |
| collection | DOAJ |
| description | Boundary conditions involving fractional derivatives of unknown functions are more general and can be used to generalize Dirichlet- or Neumann-type boundary conditions. In this article, we consider a class of nonlinear fractional differential equations having Atangana-Baleanu derivatives equipped with fractional boundary conditions. We employ some standard fixed-point theorems to establish the main results — Leray–Schauder alternative ensures the existence of solutions, whereas Banach contraction principle guarantees uniqueness. Furthermore, we present an implicit numerical scheme based on the trapezoidal method for obtaining a precise numerical estimation of the solution. Some examples are given to illustrate our analytical results and numerical findings. The main distinctive features of this work are as follows. (i) Some important properties of higher-order Atangana-Baleanu operators are introduced. (ii) Fractional boundary conditions are considered for the first time. (iii) A numerical approximation for the solution is expounded. |
| first_indexed | 2024-04-09T19:01:13Z |
| format | Article |
| id | doaj.art-6403ed464c0644699a78d67550ef0ad9 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-09T19:01:13Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-6403ed464c0644699a78d67550ef0ad92023-04-08T05:10:37ZengElsevierAlexandria Engineering Journal1110-01682023-06-0172147155Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditionsKiran Kumar Saha0N. Sukavanam1Sonjoy Pan2Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India; Corresponding author.Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, IndiaDepartment of Mathematics, Swami Vivekananda University, Kolkata, West Bengal 700121, IndiaBoundary conditions involving fractional derivatives of unknown functions are more general and can be used to generalize Dirichlet- or Neumann-type boundary conditions. In this article, we consider a class of nonlinear fractional differential equations having Atangana-Baleanu derivatives equipped with fractional boundary conditions. We employ some standard fixed-point theorems to establish the main results — Leray–Schauder alternative ensures the existence of solutions, whereas Banach contraction principle guarantees uniqueness. Furthermore, we present an implicit numerical scheme based on the trapezoidal method for obtaining a precise numerical estimation of the solution. Some examples are given to illustrate our analytical results and numerical findings. The main distinctive features of this work are as follows. (i) Some important properties of higher-order Atangana-Baleanu operators are introduced. (ii) Fractional boundary conditions are considered for the first time. (iii) A numerical approximation for the solution is expounded.http://www.sciencedirect.com/science/article/pii/S111001682300245426A3334A0834K3765L10 |
| spellingShingle | Kiran Kumar Saha N. Sukavanam Sonjoy Pan Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions Alexandria Engineering Journal 26A33 34A08 34K37 65L10 |
| title | Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions |
| title_full | Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions |
| title_fullStr | Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions |
| title_full_unstemmed | Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions |
| title_short | Existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions |
| title_sort | existence and uniqueness of solutions to fractional differential equations with fractional boundary conditions |
| topic | 26A33 34A08 34K37 65L10 |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823002454 |
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