Analytical and numerical techniques for solving a fractional integro-differential equation in complex space
In this article, we describe the existence and uniqueness of a solution to the nonlinear fractional Volterra integro differential equation in complex space using the fixed-point theory. We also examine the remarkably effective Euler wavelet method, which converts the model to a matrix structure that...
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241543?viewType=HTML |
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| author | Amnah E. Shammaky Eslam M. Youssef |
| author_facet | Amnah E. Shammaky Eslam M. Youssef |
| author_sort | Amnah E. Shammaky |
| collection | DOAJ |
| description | In this article, we describe the existence and uniqueness of a solution to the nonlinear fractional Volterra integro differential equation in complex space using the fixed-point theory. We also examine the remarkably effective Euler wavelet method, which converts the model to a matrix structure that lines up with a system of algebraic linear equations; this method then provides approximate solutions for the given problem. The proposed technique demonstrates superior accuracy in numerical solutions when compared to the Euler wavelet method. Although we provide two cases of computational methods using MATLAB R2022b, which could be the final step in confirming the theoretical investigation. |
| format | Article |
| id | doaj-art-c5a7fe6f162645deb8e4885505dd2a5a |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-c5a7fe6f162645deb8e4885505dd2a5a2025-08-20T01:53:36ZengAIMS PressAIMS Mathematics2473-69882024-11-01911321383215610.3934/math.20241543Analytical and numerical techniques for solving a fractional integro-differential equation in complex spaceAmnah E. Shammaky 0Eslam M. Youssef11. Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia2. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria 21256, EgyptIn this article, we describe the existence and uniqueness of a solution to the nonlinear fractional Volterra integro differential equation in complex space using the fixed-point theory. We also examine the remarkably effective Euler wavelet method, which converts the model to a matrix structure that lines up with a system of algebraic linear equations; this method then provides approximate solutions for the given problem. The proposed technique demonstrates superior accuracy in numerical solutions when compared to the Euler wavelet method. Although we provide two cases of computational methods using MATLAB R2022b, which could be the final step in confirming the theoretical investigation.https://www.aimspress.com/article/doi/10.3934/math.20241543?viewType=HTMLfractional calculuscomplex planefixed point theoremrationalized haar waveleteuler wavelet method |
| spellingShingle | Amnah E. Shammaky Eslam M. Youssef Analytical and numerical techniques for solving a fractional integro-differential equation in complex space AIMS Mathematics fractional calculus complex plane fixed point theorem rationalized haar wavelet euler wavelet method |
| title | Analytical and numerical techniques for solving a fractional integro-differential equation in complex space |
| title_full | Analytical and numerical techniques for solving a fractional integro-differential equation in complex space |
| title_fullStr | Analytical and numerical techniques for solving a fractional integro-differential equation in complex space |
| title_full_unstemmed | Analytical and numerical techniques for solving a fractional integro-differential equation in complex space |
| title_short | Analytical and numerical techniques for solving a fractional integro-differential equation in complex space |
| title_sort | analytical and numerical techniques for solving a fractional integro differential equation in complex space |
| topic | fractional calculus complex plane fixed point theorem rationalized haar wavelet euler wavelet method |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241543?viewType=HTML |
| work_keys_str_mv | AT amnaheshammaky analyticalandnumericaltechniquesforsolvingafractionalintegrodifferentialequationincomplexspace AT eslammyoussef analyticalandnumericaltechniquesforsolvingafractionalintegrodifferentialequationincomplexspace |