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Quantum calculus on finite intervals and applications to impulsive difference equations
In this paper we initiate the study of quantum calculus on finite intervals. We define the qk-derivative and qk-integral of a function and prove their basic properties. As an application, we proveExpand
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Quantum integral inequalities on finite intervals
In this paper, some of the most important integral inequalities of analysis are extended to quantum calculus. These include the Hölder, Hermite-Hadamard, trapezoid, Ostrowski,Expand
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Some New Riemann-Liouville Fractional Integral Inequalities
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Expand
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New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations
In this paper we define new concepts of fractional quantum calculus by defining a new q-shifting operator. After giving the basic properties we define the q-derivative and q-integral. New definitionsExpand
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Quantum integral inequalities for convex functions
In this paper we establish some new quantum integral inequalities for convex functions.
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Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions
In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theoremsExpand
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Nonlinear second-order impulsive q-difference Langevin equation with boundary conditions
In this paper, we discuss the existence and uniqueness of solutions for Langevinimpulsive q-difference equations with boundary conditions. Our studyrelies on Banach’s and Schaefer’s fixed pointExpand
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A Study of nonlinear fractional-order boundary Value Problem with nonlocal Erdelyi-Kober and generalized Riemann-Liouville Type integral boundary conditions
We investigate a new kind of nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with integral boundary conditions involving Erdelyi-Kober and generalized Riemann-Liouville fractional integrals. Expand
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Positive Solutions of a Nonlinear Three-Point Integral Boundary Value Problem
We study the existence of positive solutions to the three-point integral boundary value problem , , , , where and . We show the existence of at least one positive solution if f is either superlinearExpand
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