Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces
المؤلفون المشاركون
Derbazi, Choukri
Baitiche, Zidane
N’Guérékata, G.
Benchohra, Mouffak
المصدر
International Journal of Differential Equations
العدد
المجلد 2020، العدد 2020 (31 ديسمبر/كانون الأول 2020)، ص ص. 1-16، 16ص.
الناشر
Hindawi Publishing Corporation
تاريخ النشر
2020-10-14
دولة النشر
مصر
عدد الصفحات
16
التخصصات الرئيسية
الملخص EN
Our aim in this paper is to investigate the existence, uniqueness, and Mittag–Leffler–Ulam stability results for a Cauchy problem involving ψ-Caputo fractional derivative with positive constant coefficient in Banach and Fréchet Spaces.
The techniques used are a variety of tools for functional analysis.
More specifically, we apply Weissinger’s fixed point theorem and Banach contraction principle with respect to the Chebyshev and Bielecki norms to obtain the uniqueness of solution on bounded and unbounded domains in a Banach space.
However, a new fixed point theorem with respect to Meir–Keeler condensing operators combined with the technique of Hausdorff measure of noncompactness is used to investigate the existence of a solution in Banach spaces.
After that, by means of new generalizations of Grönwall’s inequality, the Mittag–Leffler–Ulam stability of the proposed problem is studied on a compact interval.
Meanwhile, an extension of the well-known Darbo’s fixed point theorem in Fréchet spaces associated with the concept of measures of noncompactness is applied to obtain the existence results for the problem at hand.
Finally, as applications of the theoretical results, some examples are given to illustrate the feasibility of the main theorems.
نمط استشهاد جمعية علماء النفس الأمريكية (APA)
Derbazi, Choukri& Baitiche, Zidane& Benchohra, Mouffak& N’Guérékata, G.. 2020. Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces. International Journal of Differential Equations،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1169958
نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)
Derbazi, Choukri…[et al.]. Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces. International Journal of Differential Equations No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1169958
نمط استشهاد الجمعية الطبية الأمريكية (AMA)
Derbazi, Choukri& Baitiche, Zidane& Benchohra, Mouffak& N’Guérékata, G.. Existence, Uniqueness, and Mittag–Leffler–Ulam Stability Results for Cauchy Problem Involving ψ-Caputo Derivative in Banach and Fréchet Spaces. International Journal of Differential Equations. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1169958
نوع البيانات
مقالات
لغة النص
الإنجليزية
الملاحظات
Includes bibliographical references
رقم السجل
BIM-1169958
قاعدة معامل التأثير والاستشهادات المرجعية العربي "ارسيف Arcif"
أضخم قاعدة بيانات عربية للاستشهادات المرجعية للمجلات العلمية المحكمة الصادرة في العالم العربي
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