Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint
This manuscript investigates a constrained problem of an arbitrary (fractional) order quadratic functional integro-differential equation with a quadratic functional integro-differential constraint. We demonstrate that there is at least one solution <inline-formula><math xmlns="http://w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/12/835 |
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| author | Ahmed M. A. El-Sayed Antisar A. A. Alhamali Eman M. A. Hamdallah Hanaa R. Ebead |
| author_facet | Ahmed M. A. El-Sayed Antisar A. A. Alhamali Eman M. A. Hamdallah Hanaa R. Ebead |
| author_sort | Ahmed M. A. El-Sayed |
| collection | DOAJ |
| description | This manuscript investigates a constrained problem of an arbitrary (fractional) order quadratic functional integro-differential equation with a quadratic functional integro-differential constraint. We demonstrate that there is at least one solution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>∈</mo><mi>C</mi><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></semantics></math></inline-formula> to the problem. Moreover, we outline the necessary demands for the solution’s uniqueness. In addition, the continuous dependence of the solution and the Hyers–Ulam stability of the problem are analyzed. In order to illustrate our results, we provide some particular cases and instances. |
| first_indexed | 2024-03-08T20:46:07Z |
| format | Article |
| id | doaj.art-d26dc006cd0a4d1485d5032d26fda015 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-08T20:46:07Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d26dc006cd0a4d1485d5032d26fda0152023-12-22T14:09:54ZengMDPI AGFractal and Fractional2504-31102023-11-0171283510.3390/fractalfract7120835Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential ConstraintAhmed M. A. El-Sayed0Antisar A. A. Alhamali1Eman M. A. Hamdallah2Hanaa R. Ebead3Faculty of Science, Alexandria University, Alexandria 21521, EgyptFaculty of Science, Al-Zaytoonah University, Bani Walid 38645, LibyaFaculty of Science, Alexandria University, Alexandria 21521, EgyptFaculty of Science, Alexandria University, Alexandria 21521, EgyptThis manuscript investigates a constrained problem of an arbitrary (fractional) order quadratic functional integro-differential equation with a quadratic functional integro-differential constraint. We demonstrate that there is at least one solution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>x</mi><mo>∈</mo><mi>C</mi><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></semantics></math></inline-formula> to the problem. Moreover, we outline the necessary demands for the solution’s uniqueness. In addition, the continuous dependence of the solution and the Hyers–Ulam stability of the problem are analyzed. In order to illustrate our results, we provide some particular cases and instances.https://www.mdpi.com/2504-3110/7/12/835constrained problemfunctional integro-differential equationfractional orderSchauder fixed-point theoremcontinuous dependence |
| spellingShingle | Ahmed M. A. El-Sayed Antisar A. A. Alhamali Eman M. A. Hamdallah Hanaa R. Ebead Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint Fractal and Fractional constrained problem functional integro-differential equation fractional order Schauder fixed-point theorem continuous dependence |
| title | Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint |
| title_full | Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint |
| title_fullStr | Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint |
| title_full_unstemmed | Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint |
| title_short | Qualitative Aspects of a Fractional-Order Integro-Differential Equation with a Quadratic Functional Integro-Differential Constraint |
| title_sort | qualitative aspects of a fractional order integro differential equation with a quadratic functional integro differential constraint |
| topic | constrained problem functional integro-differential equation fractional order Schauder fixed-point theorem continuous dependence |
| url | https://www.mdpi.com/2504-3110/7/12/835 |
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