Results on neutral differential equation of sobolev type with nonlocal conditions. (May 2022)

• Record Type: Journal Article
• Authors: Kalimuthu, K.; Mohan, M.; Chokkalingam, R.; Nisar, Kottakkaran Sooppy
• Is Part Of: Chaos, solitons and fractals. Volume 158(2022)
• Publication Date: 2022-05
• Subjects: MSC2010: 34B10 -- 47H10 -- 34 K40; Fractional differential equation -- Analytic semigroup -- Fixed point theorem -- Nonlocal conditions -- Faedo Galerkin approximation -- Sobolev type; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112060
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this work, we analyse the study of neutral fractional differential equation in an arbitrary Hilbert space. An associated integral equation is studied and approximate integral equation is obtained. We demonstrate the existence and uniqueness of an approximate solution by using analytic semigroup theory and the Fixed point method. In the application part, we discuss the approximation and the convergence results for such an approximation. Highlights: We analyse the study of neutral fractional differential equation in an arbitrary Hilbert space. An associated integral equation is studied and approximate integral equation is obtained. We demonstrate the existence and uniqueness of an approximate solution by using analytic semigroup theory and the fixed-point method. In the application part, we discuss the approximation and the convergence results for such an approximation.