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Implementation of q-calculus on q-integro-differential equation involving anti-periodic boundary conditions with three criteria

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  • Alam, Mehboob
  • Zada, Akbar

Abstract

In the present article, by using the Caputo type fractional q-derivative, we investigate the existence of solution for q-integro-differential equationcDqαu(σ)+ϕ(σ,u(σ),u′(σ),u″(σ),cDqβ1u(σ),cDqβ2u(σ),∫0σ1f(s)u(s)dqs,∫σ1σf(s)u(s)dqs)=0,involving anti-periodic boundary conditions with three criteria. By employing the α-admissible map and fixed point theory, sufficient conditions are established to ensure the existence of solution for the addressed equation. Examples involving pseudo-codes and tables are presented to demonstrate the validity of our theoretical findings.

Suggested Citation

  • Alam, Mehboob & Zada, Akbar, 2022. "Implementation of q-calculus on q-integro-differential equation involving anti-periodic boundary conditions with three criteria," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s0960077921009796
    DOI: 10.1016/j.chaos.2021.111625
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    References listed on IDEAS

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    1. Danfeng Luo & Mehboob Alam & Akbar Zada & Usman Riaz & Zhiguo Luo & Peter Giesl, 2021. "Existence and Stability of Implicit Fractional Differential Equations with Stieltjes Boundary Conditions Involving Hadamard Derivatives," Complexity, Hindawi, vol. 2021, pages 1-36, March.
    2. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Yulin Zhao & Guobing Ye & Haibo Chen, 2013. "Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional -Derivatives Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, February.
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    Cited by:

    1. Binlin Zhang & Rafia Majeed & Mehboob Alam, 2022. "On Fractional Langevin Equations with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    2. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.

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