ON KATUGAMPOLA FRACTIONAL q-INTEGRAL AND q-DERIVATIVE


By

Lata Chanchlani1, Subhash Alha2 and Ishfaq Ahmad Mallah3

1Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India

2,3Department of Mathematics, Maulana Azad National Urdu university, Hyderabad-500032, Telangana, India

Email:chanchlani281106@gmail.com, subhashalha@manuu.edu.in, ishfaqmalla@gmail.com

(Received : September 01, 2021; In format : September 28, 2021; Revised in final form : March 28, 2022)


Abstract

We first study Katugampola fractional q-integral and q-derivative in the space L1qp [a, b] and obtain some properties of these operators, which include the image of power function, semi group property and composition of these operators. Next, we look at the existence and uniqueness of solution to generalized fractional q-Cauchy type problems involving Katugampola fractional q-derivative. Also, we obtain their compact form solutions using Adomian decomposition method, in terms of q-Mittag-Leffler type functions.


2020 Mathematical Sciences Classification: 26A33, 39A13.

Keywords and Phrases: Fractional q-integral, Fractional q-derivative, Adomian decomposition method; q-difference



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