Existence and Stability Results for Impulsive Fractional <i>q</i>-Difference Equation

Abstract

In this paper, we study the boundary value problem for an impulsive fractional q-difference equation. Based on Banach's contraction mapping principle, the existence and Hyers-Ulam stability of solutions for the equation which we considered are obtained. At last, an illustrative example is given for the main result.

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

“…Table 2 Numerical results of q (θ + 1) and k * of FDq -DP (21) with q ∈ { 3 10 , 1 2 , 9 10 } in Example 5.1…”

“…In this sense, several interesting topics concerning research for differential equations involving fractional quantum calculus have been devoted to the existence and the Ulam-Hyers stability of the solutions. Recently, many interesting results concerning the existence and Ulam-type stability of solutions for differential equations with fractional q-calculus have been obtained, see [8][9][10][11] and the references therein. In [12,13], the existence and uniqueness of solutions were investigated for sequential differential equations with q-fractional calculus.…”

A coupled system of q-fractional Lane-Emden problem involving three sequential q-fractional derivatives with stability inequality

“…On the other hand, the differential equations involving fractional q−calculus plays an important role in quantum calculus, recently, there has been a very important progress in the study of the theory of fractional q−differential equations, see for example [2,9,18,20,28] and the references cited therein. Recently, Many scholars have studied the existence and uniqueness and Ulam-stability (U-S) of solutions of differential equations involving fractional quantum calculus (FQC), see the works [5,9,19,25] and the references cited therein. The singular fractional q−differential equations (Fq − DE) are also very important in applied sciences, see for example [4,21,27,28].…”

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

“…Due to its importance and application in several mathematical models of real phenomena, particularly in the control theory and biological or medical fields as observe blood flow phenomena. Recently, many authors investigated existence of solutions for impulsive fractional q-difference equations; see [4,20,23,32] for example.…”