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A perturbed quadratic equation involving Erdélyi–Kober fractional integral

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In the Banach space of real functions which are defined, bounded and continuous on an unbounded interval, we study the solvability of a perturbed Erdélyi–Kober fractional quadratic integral equation.

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References

  1. Appell, J., Zabrejko, P.P.: Nonlinear superposition operators. Cambridge tracts in mathematics, 95. Cambridge University Press, Cambridge (1990)

    Book  Google Scholar 

  2. Argyros, I.K.: Quadratic equations and applications to Chandrasekhar’s and related equations. Bull. Austral. Math. Soc. 32, 275–292 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boffi, V.C., Spiga, G.: An equation of Hammerstein type arising in particle transport theory. J. Math. Phys. 24, 1625–1629 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  4. Caballero, J., O’Regan, D., Sadarangani, K.: On solutions of an integral equation related to traffic flow on unbounded domains. Arch. Math. (Basel) 82, 551–563 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chandrasekher, S.: Radiative transfer. Dover Publications, New York (1960)

    Google Scholar 

  6. Darwish, M.A.: On quadratic integral equation of fractional orders. J. Math. Anal. Appl. 311, 112–119 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Spiga, G., Bowden, R.L., Boffi, V.C.: On the solutions of a class of nonlinear integral equations arising in transport theory. J. Math. Phys. 25, 3444–3450 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  8. Stuart, C.A.: Existence theorems for a class of nonlinear integral equations. Math. Z. 137, 49–66 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  9. Garra, R., Giusti, A., Mainardi, F., Pagnini, G.: Fractional relaxation with time-varying coefficient. Fract. Calc. Appl. Anal. 17(2), 424–439 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Herrmann, R.: Reflection symmetric Erdélyi–Kober type operators—a quasi-particle interpretation. Fract. Calc. Appl. Anal. 17(4), 1215–1228 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kiryakova, V.: Convolutions of Erdélyi–Kober fractional integration operators, complex analysis and applications ’87 (Varna, 1987), pp. 273–283. Publ. House Bulgar. Acad. Sci, Sofia (1989)

  12. Pagnini, G.: Erdélyi–Kober fractional diffusion. Fract. Calc. Appl. Anal. 15(1), 117–127 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sneddon, I.N.: Mixed boundary value problems in potential theory. North-Holland Publ, Amsterdam (1966)

    MATH  Google Scholar 

  14. Alamo, J.A., Rodríguez, J.: Operational calculus for modified Erdélyi–Kober operators. Serdica Bulgaricae Mathematicae Publicationes 20, 351–363 (1994)

    MathSciNet  MATH  Google Scholar 

  15. Darwish, M.A., Sadarangani, K.: On a quadratic integral equation with supremum involving Erdélyi–Kober fractional order. Math. Nachr. 228(5–6), 566–576 (2015)

  16. Kiryakova, V.: Generalized fractional calculus and applications. Longman Sci. & Techn., Harlow and Wiley, New York (1994)

  17. Kiryakova, V.S., Al-Saqabi, B.N.: Transmutation method for solving Erdélyi–Kober fractional differintegral equations. J. Math. Anal. Appl. 211, 347–364 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  18. Banaś, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Lecture notes in pure and applied mathematics, vol. 60. Marcel Dekker, New York (1990)

    Google Scholar 

  19. Banaś, J.: Measures of noncompactness in the space of continuous tempered functions. Demonstratio Math. 14, 127–133 (1981)

    MathSciNet  MATH  Google Scholar 

  20. Banaś, J., Olszpwz, L.: Measures of noncompactness related to monotonicity. Comment. Math. 41, 13–23 (2001)

    MathSciNet  MATH  Google Scholar 

  21. Darbo, G.: Punti uniti in trasformazioni a codominio non compatto. Rend. Sem. Mat. Univ. Padova 24, 84–92 (1955)

    MathSciNet  MATH  Google Scholar 

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Acknowledgments

The third author was partially supported by the project MTM2013-44357-P.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017, Las Palmas, Spain

    Josefa Caballero & Kishin Sadarangani

  2. Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia

    Mohamed Abdalla Darwish

  3. Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt

    Mohamed Abdalla Darwish

Authors
  1. Josefa Caballero
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  2. Mohamed Abdalla Darwish
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  3. Kishin Sadarangani
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Correspondence to Mohamed Abdalla Darwish.

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Caballero, J., Darwish, M.A. & Sadarangani, K. A perturbed quadratic equation involving Erdélyi–Kober fractional integral. RACSAM 110, 541–555 (2016). https://doi.org/10.1007/s13398-015-0246-2

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  • DOI: https://doi.org/10.1007/s13398-015-0246-2

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