Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations
In the recent past, multi-term fractional equations have been studied using symmetry methods. In some cases, many practical test problems with some symmetries are provided to demonstrate the authenticity and utility of the used techniques. Fractional-order differential equations can be formulated by...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1342 |
| _version_ | 1797415383419846656 |
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| author | Dildar Ahmad Ravi P. Agarwal Ghaus ur Rahman |
| author_facet | Dildar Ahmad Ravi P. Agarwal Ghaus ur Rahman |
| author_sort | Dildar Ahmad |
| collection | DOAJ |
| description | In the recent past, multi-term fractional equations have been studied using symmetry methods. In some cases, many practical test problems with some symmetries are provided to demonstrate the authenticity and utility of the used techniques. Fractional-order differential equations can be formulated by using two types of differential operators: single-term and multi-term differential operators. Boundary value problems with single- as well as multi-term differential operators have been extensively studied, but several multi-term fractional differential equations still need to be formulated, and examination should be done with symmetry or any other feasible techniques. Therefore, the purpose of the present research work is the formulation and study of a new couple system of multi-term fractional differential equations with delay, as well as supplementation with nonlocal boundary conditions. After model formulation, the existence of a solution and the uniqueness conditions will be developed, utilizing fixed point theory and functional analysis. Moreover, results related to Ulam’s and other types of functional stability will be explored, and an example is carried out to illustrate the findings of the work. |
| first_indexed | 2024-03-09T05:47:51Z |
| format | Article |
| id | doaj.art-196c4b5bcd89472c8e6fe82c6fd19bcf |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:47:51Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-196c4b5bcd89472c8e6fe82c6fd19bcf2023-12-03T12:19:29ZengMDPI AGSymmetry2073-89942022-06-01147134210.3390/sym14071342Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential EquationsDildar Ahmad0Ravi P. Agarwal1Ghaus ur Rahman2Department of Mathematics & Statistics, University of Swat, Mingora 19130, PakistanDepartment of Mathematics, Texas A & M University Kingsville, Kingsville, TX 78363, USADepartment of Mathematics & Statistics, University of Swat, Mingora 19130, PakistanIn the recent past, multi-term fractional equations have been studied using symmetry methods. In some cases, many practical test problems with some symmetries are provided to demonstrate the authenticity and utility of the used techniques. Fractional-order differential equations can be formulated by using two types of differential operators: single-term and multi-term differential operators. Boundary value problems with single- as well as multi-term differential operators have been extensively studied, but several multi-term fractional differential equations still need to be formulated, and examination should be done with symmetry or any other feasible techniques. Therefore, the purpose of the present research work is the formulation and study of a new couple system of multi-term fractional differential equations with delay, as well as supplementation with nonlocal boundary conditions. After model formulation, the existence of a solution and the uniqueness conditions will be developed, utilizing fixed point theory and functional analysis. Moreover, results related to Ulam’s and other types of functional stability will be explored, and an example is carried out to illustrate the findings of the work.https://www.mdpi.com/2073-8994/14/7/1342fractional differential equationsmulti-term operatorsexistence and uniqueness of solutionfunctional stabilitydelay term |
| spellingShingle | Dildar Ahmad Ravi P. Agarwal Ghaus ur Rahman Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations Symmetry fractional differential equations multi-term operators existence and uniqueness of solution functional stability delay term |
| title | Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations |
| title_full | Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations |
| title_fullStr | Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations |
| title_full_unstemmed | Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations |
| title_short | Formulation, Solution’s Existence, and Stability Analysis for Multi-Term System of Fractional-Order Differential Equations |
| title_sort | formulation solution s existence and stability analysis for multi term system of fractional order differential equations |
| topic | fractional differential equations multi-term operators existence and uniqueness of solution functional stability delay term |
| url | https://www.mdpi.com/2073-8994/14/7/1342 |
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