Mild solutions for conformable fractional order functional evolution equations via Meir-Keeler type fixed point theorem

Abstract

In this study, we delve into the realm of mild solutions for conformable fractional order functional evolution equations, focusing on cases where the fractional order is strictly greater than $1$ and less than $2$  within a separable Banach space. We demonstrate the existence, uniqueness, attractiveness, and controllability of these solutions under local conditions. Our approach involves leveraging a contribution of Meir-Keeler's fixed point theorem alongside the principle of measures of noncompactness. To demonstrate the practical ramifications of our theoretical finds, we provide a specific example that underscores the relevance and applications of the established results. TRANSLATE with x EnglishArabicHebrewPolishBulgarianHindiPortugueseCatalanHmong DawRomanianChinese SimplifiedHungarianRussianChinese TraditionalIndonesianSlovakCzechItalianSlovenianDanishJapaneseSpanishDutchKlingonSwedishEnglishKoreanThaiEstonianLatvianTurkishFinnishLithuanianUkrainianFrenchMalayUrduGermanMalteseVietnameseGreekNorwegianWelshHaitian CreolePersian   TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster PortalBack