Abstract
In this paper, the new concepts of Hahn difference operators are introduced. The properties of fractional Hahn calculus in the sense of a forward Hahn difference operator are introduced and developed.
Highlights
The quantum calculus, known as calculus without the consideration of limits, involves sets of non-differentiable functions
The aim of this paper is to introduce new concepts of Hahn difference operator, the fractional Hahn integral, the fractional Hahn difference operators of Riemann-Liouville and Caputo types
In the theorems we introduce the properties of fractional Hahn integral as the following theorem
Summary
The quantum calculus, known as calculus without the consideration of limits, involves sets of non-differentiable functions. Hamza et al [ – ] studied the theory of linear Hahn difference equations They established the existence and uniqueness results for the initial value problems for Hahn difference equations by using the method of successive approximations. They proved Gronwall’s and Bernoulli’s inequalities with respect to the Hahn difference operator and investigated the mean value theorems, Leibniz’s rule and Fubini’s theorem for this calculus. [ω , T]q,ω × R × R → R is a continuous function, and φ : C([ω , T]q,ω, R) → R is a given functional In this year , Sriphanomwan et al [ ] studied a nonlocal boundary value problem for second-order nonlinear Hahn integro-difference equation with integral boundary condition.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
