$q$- Analogue of the Karry-Kalim-Adnan transform with applications to q-differential equations
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Abstract
This work analyzes certain features of the Karry-Kalim-Adnan transform and discusses its $q$-analogues in a quantum calculus theory. It discusses a number of characteristics of the $q$-Karry-Kalim-Adnan transform and its application to a wide range of functions, including $q$- trigonometric,$q$- hyperbolic and $q$-exponential functions and some $q$-polynomials. Additionally, it utilizes First- and second-order $q$-initial value problems to illustrate effectiveness and performance of our proposed $q$-transform analogues. Over and above, the paper proves the $q$-convolution theorem and provides a number of tables to further ease the $q$- transform technique in solving various ostensibly $q$-initial value problems.
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