Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative
Creators
- 1. University of Malakand
- 2. American University of the Middle East
- 3. Prince Sultan University
- 4. Suan Dusit University
- 5. King Mongkut's University of Technology North Bangkok
- 6. King Khalid University
Description
This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.
Translated Descriptions
Translated Description (Arabic)
هذه المقالة مخصصة للتحقيق في فئة من مشكلة القيمة الأولية غير المحلية للمعادلات التفاضلية الكسرية الضمنية (IFDEs) بمشاركة المشتق الكسري Caputo - Fabrizio (CFFD). من خلال نظرية النقطة الثابتة لكراسنوسيلسكي ومبدأ انكماش بنك، يتم الحصول على نتائج الوجود والتفرد. علاوة على ذلك، نحدد بعض نتائج استقرار Hyers - Ulam (H - U) و Hyers - Ulam (g - H - U) المعمم. أخيرًا، يتم تقديم مثال لإظهار نتائجنا.
Translated Description (English)
This article is devoted to investigating a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.
Translated Description (French)
This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.
Translated Description (Spanish)
This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.
Additional details
Additional titles
- Translated title (Arabic)
- دراسة المعادلات التفاضلية الاندفاعية الضمنية التي تتضمن المشتق الكسري Caputo - Fabrizio
- Translated title (English)
- Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative
- Translated title (French)
- Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivtive
- Translated title (Spanish)
- Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative
Identifiers
- Other
- https://openalex.org/W4205189726
- DOI
- 10.3934/math.2022222
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