Existence and stability analysis for a class of fractional pantograph q-difference equations with nonlocal boundary conditions

Abstract

In this present manuscript, by applying fractional quantum calculus, we study a nonlinear fractional pantograph q-difference equation with nonlocal boundary conditions. We prove the existence and uniqueness results by using the well-known fixed-point theorems of Schaefer and Banach. We also discuss the Ulam–Hyers stability of the mentioned pantograph q-difference problem. Lastly, the paper includes pertinent examples to support our theoretical analysis and justify the validity of the results.

Existence and Ulam Stability of Initial Value Problem for Impulsive Fractional q-Difference Equations

“…As a result, fractional q-difference equations have become an attractive subject and have received a lot of attention from scholars in recent years (see [2,4,5,9]). Many researchers have also investigated the existence and Ulam stability of solutions to initial and boundary value problems for fractional q-difference equations involving the Caputo fractional q-derivative; see [1,6,16,22] and the references therein.…”

“…The Hyers theorem was generalised by Rassias [26] in 1978, allowing the Cauchy difference to be unbounded. Following this finding, numerous mathematicians were drawn to and inspired to look into the Ulam-Hyers stability and Ulam-Hyersrassias stability of fractional differential equations and fractional q-difference equations; see the papers [1,16,20,22,27,28,31] and the references therein.…”