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Certain Inequalities Involving the Fractional q‐Integral Operators

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  • Dumitru Baleanu
  • Praveen Agarwal

Abstract

We establish some inequalities involving Saigo fractional q‐integral operator in the theory of quantum calculus by using the two parameters of deformation, q1 and q2, whose special cases are shown to yield corresponding inequalities associated with Riemann‐Liouville and Kober fractional q‐integral operators, respectively. Furthermore, we also consider their relevance with other related known results.

Suggested Citation

  • Dumitru Baleanu & Praveen Agarwal, 2014. "Certain Inequalities Involving the Fractional q‐Integral Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:371274
    DOI: 10.1155/2014/371274
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    References listed on IDEAS

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    1. Dumitru Baleanu & Praveen Agarwal, 2014. "Certain Inequalities Involving the Fractional -Integral Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    2. D. Baleanu & S. D. Purohit, 2014. "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, April.
    3. D. Baleanu & S. D. Purohit, 2014. "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
    5. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    Cited by:

    1. Guangzhou Li & Feixiang Chen, 2014. "Hermite‐Hadamard Type Inequalities for Superquadratic Functions via Fractional Integrals," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. D. Baleanu & S. D. Purohit, 2014. "Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Haile Habenom & D. L. Suthar & Melaku Gebeyehu, 2019. "Application of Laplace Transform on Fractional Kinetic Equation Pertaining to the Generalized Galué Type Struve Function," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    4. Junesang Choi & Praveen Agarwal, 2014. "Some New Saigo Type Fractional Integral Inequalities and Their q‐Analogues," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Sotiris K. Ntouyas & Sunil D. Purohit & Jessada Tariboon, 2014. "Certain Chebyshev Type Integral Inequalities Involving Hadamard’s Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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