A Numerical Approach for Dealing with Fractional Boundary Value Problems
This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of order <inline-formula><math xmlns="http:...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/19/4082 |
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| author | Abeer A. Al-Nana Iqbal M. Batiha Shaher Momani |
| author_facet | Abeer A. Al-Nana Iqbal M. Batiha Shaher Momani |
| author_sort | Abeer A. Al-Nana |
| collection | DOAJ |
| description | This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and the fractional central formula for approximating the Caputo differentiator of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>α</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The first formula is recalled here, whereas the second one is derived based on the generalized Taylor theorem. The stability of the proposed approach is investigated in view of some formulated results. In addition, several numerical examples are included to illustrate the efficiency and applicability of our approach. |
| first_indexed | 2024-03-10T21:39:59Z |
| format | Article |
| id | doaj.art-93308158398b40f685a100853ab109b9 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:39:59Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-93308158398b40f685a100853ab109b92023-11-19T14:43:07ZengMDPI AGMathematics2227-73902023-09-011119408210.3390/math11194082A Numerical Approach for Dealing with Fractional Boundary Value ProblemsAbeer A. Al-Nana0Iqbal M. Batiha1Shaher Momani2Department of Mathematics, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi ArabiaDepartment of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, JordanNonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab EmiratesThis paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> and the fractional central formula for approximating the Caputo differentiator of order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>α</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. The first formula is recalled here, whereas the second one is derived based on the generalized Taylor theorem. The stability of the proposed approach is investigated in view of some formulated results. In addition, several numerical examples are included to illustrate the efficiency and applicability of our approach.https://www.mdpi.com/2227-7390/11/19/4082fractional boundary value problemfractional central formulasCaputo differentiator |
| spellingShingle | Abeer A. Al-Nana Iqbal M. Batiha Shaher Momani A Numerical Approach for Dealing with Fractional Boundary Value Problems Mathematics fractional boundary value problem fractional central formulas Caputo differentiator |
| title | A Numerical Approach for Dealing with Fractional Boundary Value Problems |
| title_full | A Numerical Approach for Dealing with Fractional Boundary Value Problems |
| title_fullStr | A Numerical Approach for Dealing with Fractional Boundary Value Problems |
| title_full_unstemmed | A Numerical Approach for Dealing with Fractional Boundary Value Problems |
| title_short | A Numerical Approach for Dealing with Fractional Boundary Value Problems |
| title_sort | numerical approach for dealing with fractional boundary value problems |
| topic | fractional boundary value problem fractional central formulas Caputo differentiator |
| url | https://www.mdpi.com/2227-7390/11/19/4082 |
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