Solvability of infinite system of $q$-difference equations in $c_0$ space

DIPANKAR PATGIRI; Bipan  Hazarika

doi:10.5269/bspm.78902

DIPANKAR PATGIRI Department of Mathematics, Gauhati University
Bipan Hazarika Department of Mathematics, Gauhati University

Résumé

We investigate the existence of solutions of an infinite system of fractional $q$-difference equations with integral conditions in $c_0$ space which involves a $q$-derivative of the Caputo type. The result is obtained by using a generalization of Darbo's fixed point theorem and measure of noncompactness (MNC in short). This method has demonstrated significant potential in the analysis of these types of problem. It also introduces essential elements of fractional $q$-calculus. Finally, an example is presented to validate the proposed findings.

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