Nonlocal q-Symmetric Integral Boundary Value Problem for Sequential q-Symmetric Integrodifference Equations

Abstract

In this paper, we prove the sufficient conditions for the existence results of a solution of a nonlocal q-symmetric integral boundary value problem for a sequential q-symmetric integrodifference equation by using the Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Some examples are also presented to illustrate our results.

Hilfer Fractional Quantum Derivative and Boundary Value Problems

“…Applying the Riemann-Liouville fractional q-integral of order β(1 − α) to both sides of the above equation, we deduce from (17)…”

“…Recent treatment on such material can be found in [7]. Research on the topic has yield variety of new results in recent years, as seen in [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and references therein.…”

An Existence Study on the Fractional Coupled Nonlinear q -Difference Systems via Quantum Operators along with Ulam–Hyers and Ulam–Hyers–Rassias Stability

“…So later, various mathematical q-difference fractional models of IVPs and BVPs have been presented in which different methods like the lower-upper solutions technique, fixedpoint results, and iterative methods have been implemented. For instance, we see q-intego-equation on time scales in [12], q-delay equations in [13], q-integro-equations under the q -integral conditions in [14], singular q-equations in [15], q -sequential symmetric BVPs in [16], q-difference equations having p-Laplacian in [17], four-point q-BVP with different orders in [18], oscillation on q-difference inclusions in [19], etc.…”

A novel fractional structure of a multi-order quantum multi-integro-differential problem

“…Finally, Miller [28] combined quantum differential equations with Lie theory and investigated new theoretical results in this regard. By continuing this trend in the subsequent years, numerous researchers extended this field and obtained many interesting findings on the fractional quantum differential equations and inclusions (for more details, see [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]).…”