On qualitative theory of fractional order delay evolution equation via the prior estimate method. (7th April 2020)

• Record Type: Journal Article
• Authors: Sher, Muhammad; Shah, Kamal; Rassias, John
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 10(2020)
• Page Start: 6464
• Page End: 6475
• Publication Date: 2020-04-07
• Subjects: existence and uniqueness of solutions -- fractional differential equations -- prior estimate method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6390
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this manuscript we use prior estimate method also known as the topological degree method to investigate the existence and uniqueness of solution for a class of evolution fractional order differential equations (FODEs) with proportional delay using Caputo derivative. In the same line, we will also study different kinds of Ulam stability such as Ulam‐Hyers (UH) stability, generalized Ulam‐Hyers (GUH) stability, Ulam‐Hyers‐Rassias (UHR) stability, and generalized Ulam‐Hyers‐Rassias (GUHR) stability for the considered problem. To justify our results, we provide a pertinent example.