Study of Nonlocal Multiorder Implicit Differential Equation Involving Hilfer Fractional Derivative on Unbounded Domains

Abstract

This paper aims to study the existence and uniqueness of the solution for nonlocal multiorder implicit differential equation involving Hilfer fractional derivative on unbounded domains <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mi>a</a:mi> <a:mo>,</a:mo> <a:mi>∞</a:mi> </a:mrow> </a:mfenced> <a:mo>,</a:mo> <a:mi>a</a:mi> <a:mo>≥</a:mo> <a:mn>0</a:mn> </a:math> , in an applicable Banach space by utilizing the Banach contraction principle. Furthermore, we discuss various types of stability such as Ulam–Hyers–Rassias (UHR), Ulam–Hyers (UH), and semi-Ulam–Hyers–Rassias (sUHR) for nonlocal boundary value problem. Absolutely, our results cover that several outcomes have existed in the literature.