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      Condensing Functions and Approximate Endpoint Criterion for the Existence Analysis of Quantum Integro-Difference FBVPs

      , , , , ,
      Symmetry
      MDPI AG

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          Abstract

          A nonlinear quantum boundary value problem (q-FBVP) formulated in the sense of quantum Caputo derivative, with fractional q-integro-difference conditions along with its fractional quantum-difference inclusion q-BVP are investigated in this research. To prove the solutions’ existence for these quantum systems, we rely on the notions such as the condensing functions and approximate endpoint criterion (AEPC). Two numerical examples are provided to apply and validate our main results in this research work.

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          Most cited references38

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          q-Difference Equations

          F. Jackson (1910)
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            Certain fractional q-integrals and q-derivatives

            R. AGARWAL (1969)
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              XI.—On q-Functions and a certain Difference Operator

              F. Jackson (1909)
              In this paper my object is, primarily, to investigate the properties of a certain operative symbolwhich appears to be of great utility in discussingq-functions. The first part of the paper will consist of an investigation into the various forms of and the nature of the inverse operations symbolised by Δ−n . With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function ofx.
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                Author and article information

                Contributors
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                Journal
                SYMMAM
                Symmetry
                Symmetry
                MDPI AG
                2073-8994
                March 2021
                March 12 2021
                : 13
                : 3
                : 469
                Article
                10.3390/sym13030469
                044a027d-e091-4125-8942-f505afc1b01a
                © 2021

                https://creativecommons.org/licenses/by/4.0/

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