EXISTENCE OF SOLUTION FOR IMPULSIVE FRACTIONAL [q.sub.r]-DIFFERENCE EQUATION OF IMPLICIT FORM WITH NONLOCAL BOUNDARY CONDITION

This study examines the conditions needed for the existence of solutions to an impulsive fractional [q.sub.r]-difference equation with the implicit form. The fractional derivative we analyze in the problem is of the Caputo type, which involves a q-shifting operator of the form [.sub.a][[??].sub.q](u...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 15; no. 6; p. 1460
Main Authors Kachari, P, Borah, J, Hazarika, B
Format Journal Article
LanguageEnglish
Published Turkic World Mathematical Society 01.06.2025
Subjects
Boundary value problems
Difference equations
Mathematical research
India
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Summary:This study examines the conditions needed for the existence of solutions to an impulsive fractional [q.sub.r]-difference equation with the implicit form. The fractional derivative we analyze in the problem is of the Caputo type, which involves a q-shifting operator of the form [.sub.a][[??].sub.q](u) = qu + (1 - q)a. Here, nonlocal conditions are the boundary conditions we take into account. Regarding the existence of solutions for the given problem, the result is obtained by means of Krasnoselskii's fixed point theorem. In addition, circumstances required for the Ulam-Hyers and Generalized Ulam-Hyers stability of the impulsive problem are explored. Finally, we provide an example to demonstrate our findings. Keywords: quantum calculus, implicit, impulsive fractional [q.sub.r]-difference equation, nonlocal boundary condition, Ulam-Hyers stability. AMS Subject Classification: 39A13, 26A33, 34A37, 34A09, 34B10
ISSN:2146-1147