Open AccessAPPLICABILITY OF TOPOLOGICAL DEGREE THEORY TO EVOLUTION EQUATION WITH PROPORTIONAL DELAY
Author(s) -
Muhammad Sher,
Kamal Shah,
YuMing Chu,
Rahmat Ali Khan
Publication year - 2020
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x20400289
Subject(s) - mathematics , uniqueness , degree (music) , stability (learning theory) , class (philosophy) , topology (electrical circuits) , differential equation , derivative (finance) , mathematical analysis , combinatorics , computer science , physics , machine learning , artificial intelligence , acoustics , financial economics , economics
In this paper, we use the topological degree theory (TDT) to investigate the existence and uniqueness of solution for a class of evolution fractional order differential equations (FODEs) with proportional delay using Caputo derivative under local conditions. 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 an example.