Published July 10, 2020 | Version v1
Publication Metadata-only

MATHEMATICAL ANALYSIS OF COUPLED SYSTEMS WITH FRACTIONAL ORDER BOUNDARY CONDITIONS

Creators

  • 1. University of Peshawar
  • 2. University of Malakand
  • 3. China Medical University Hospital
  • 4. China Medical University
  • 5. King Mongkut's University of Technology Thonburi

Description

In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann–Liouville fractional derivatives. The standard fixed point theorem like Leray–Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. Also, an example is given to illustrate our theoretical results. The proposed problem is the generalization of third-order ordinary differential equations with classical, initial and anti-periodic boundary conditions.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

في هذه الورقة، نثبت وجود وتفرد وأنواع مختلفة من استقرار أولام للأنظمة المقترنة بالترتيب الكسري مع شروط حدود الترتيب الكسري التي تنطوي على مشتقات كسور ريمان- ليوفيل. يتم تطبيق نظرية النقطة الثابتة القياسية مثل بديل ليراي شودر وتقلص بنك لتأسيس نظرية الوجود والتفرد. علاوة على ذلك، فإننا نبني ظروفًا كافية للاستقرار المذكور أعلاه من خلال طريقتين. لذلك، يتم إعطاء مثال لتوضيح نتائجنا النظرية. المشكلة المقترحة هي تعميم المعادلات التفاضلية العادية من الدرجة الثالثة مع شروط الحدود الكلاسيكية والأولية والمضادة للدورات.

Translated Description (English)

In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann–Liouville fractional derivatives. The standard fixed point theorem like Leray–Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. So, an example is given to illustrate our theoretical results. The proposed problem is the generalization of third-order ordinary differential equations with classical, initial and anti-periodic boundary conditions.

Translated Description (French)

In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann–Liouville fractional derivatives. The standard fixed point theorem like Leray–Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. Donc, un exemple est donné pour illustrer nos résultats théoriques. Le problème proposé est la généralisation des équations différentielles ordinaires de troisième ordre avec des conditions limites classiques, initiales et anti-périodiques.

Translated Description (Spanish)

In this paper, we prove the existence, uniqueness and various kinds of Ulam stability for fractional order coupled systems with fractional order boundary conditions involving Riemann–Liouville fractional derivatives. The standard fixed point theorem like Leray–Schauder alternative and Banach contraction are applied to establish the existence theory and uniqueness. Furthermore, we build sufficient conditions for the stability mentioned above by two methods. Por lo tanto, an example is given to illustrate our theoretical results. El problema propuesto es la generalización de las ecuaciones diferenciales ordinarias de tercer orden con condiciones límite clásicas, iniciales y antiperiódicas.

Additional details

Additional titles

Translated title (Arabic)
التحليل الرياضي للأنظمة المقترنة بشروط حدود الترتيب الكسري
Translated title (English)
MATHEMATICAL ANALYSIS OF COUPLED SYSTEMS WITH FRACTIONAL ORDER BOUNDARY CONDITIONS
Translated title (French)
ANALYSE MATHÉMATIQUE DES SYSTÈMES COUPLÉS AVEC CONDITIONS LIMITES D'ORDRE FRACTIONNAIRE
Translated title (Spanish)
ANÁLISIS MATEMÁTICO DE SISTEMAS ACOPLADOS CON CONDICIONES LÍMITE DE ORDEN FRACCIONAL

Identifiers

Other
https://openalex.org/W3023752989
DOI
10.1142/s0218348x20400125

Is supplement to
https://openalex.org/W4319083558 (Other)
https://openalex.org/W4313451036 (Other)
https://openalex.org/W4291638237 (Other)
https://openalex.org/W4224318062 (Other)
https://openalex.org/W329565398 (Other)
https://openalex.org/W3154989072 (Other)
https://openalex.org/W2947456921 (Other)
https://openalex.org/W2520698300 (Other)
https://openalex.org/W2166320748 (Other)
https://openalex.org/W138666971 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Thailand

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