Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis
In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/6/449 |
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| author | Hind H. G. Hashem Ahmed M. A. El-Sayed Shorouk M. Al-Issa |
| author_facet | Hind H. G. Hashem Ahmed M. A. El-Sayed Shorouk M. Al-Issa |
| author_sort | Hind H. G. Hashem |
| collection | DOAJ |
| description | In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mi>B</mi><mi>C</mi><mo>(</mo><msub><mi>R</mi><mo>+</mo></msub><mo>)</mo><mo>.</mo><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula> In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions. |
| first_indexed | 2024-03-11T02:27:48Z |
| format | Article |
| id | doaj.art-97d527c7f1db4de09cbd67cab789d4a4 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T02:27:48Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-97d527c7f1db4de09cbd67cab789d4a42023-11-18T10:29:27ZengMDPI AGFractal and Fractional2504-31102023-05-017644910.3390/fractalfract7060449Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-AxisHind H. G. Hashem0Ahmed M. A. El-Sayed1Shorouk M. Al-Issa2Faculty of Science, Alexandria University, Alexandria 21544, EgyptFaculty of Science, Alexandria University, Alexandria 21544, EgyptFaculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida 1600, LebanonIn this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mspace width="3.33333pt"></mspace><mi>B</mi><mi>C</mi><mo>(</mo><msub><mi>R</mi><mo>+</mo></msub><mo>)</mo><mo>.</mo><mspace width="3.33333pt"></mspace></mrow></semantics></math></inline-formula> In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions.https://www.mdpi.com/2504-3110/7/6/449hybrid integral inclusionexistence resultsmeasure of noncompactnessdarbo fixed-point theoremfractal feedback control |
| spellingShingle | Hind H. G. Hashem Ahmed M. A. El-Sayed Shorouk M. Al-Issa Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis Fractal and Fractional hybrid integral inclusion existence results measure of noncompactness darbo fixed-point theorem fractal feedback control |
| title | Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis |
| title_full | Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis |
| title_fullStr | Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis |
| title_full_unstemmed | Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis |
| title_short | Investigating Asymptotic Stability for Hybrid Cubic Integral Inclusion with Fractal Feedback Control on the Real Half-Axis |
| title_sort | investigating asymptotic stability for hybrid cubic integral inclusion with fractal feedback control on the real half axis |
| topic | hybrid integral inclusion existence results measure of noncompactness darbo fixed-point theorem fractal feedback control |
| url | https://www.mdpi.com/2504-3110/7/6/449 |
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