ON URYSOHN-VOLTERRA FRACTIONAL QUADRATIC INTEGRAL EQUATIONS

Mohamed Abdalla Darwish; John R. Graef; Kishin Sadarangani

doi:10.11948/2018.331

2018 Volume 8 Issue 1

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Mohamed Abdalla Darwish, John R. Graef, Kishin Sadarangani. ON URYSOHN-VOLTERRA FRACTIONAL QUADRATIC INTEGRAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 331-343. doi: 10.11948/2018.331

Citation:

Mohamed Abdalla Darwish, John R. Graef, Kishin Sadarangani. ON URYSOHN-VOLTERRA FRACTIONAL QUADRATIC INTEGRAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 331-343. doi: 10.11948/2018.331

ON URYSOHN-VOLTERRA FRACTIONAL QUADRATIC INTEGRAL EQUATIONS

1 Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt;
2 Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA;
3 Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain

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Abstract

Abstract

In this paper the authors study a fractional quadratic integral equation of Urysohn-Volterra type. They show that the integral equation has at least one monotonic solution in the Banach space of all real functions defined and continuous on the interval[0,1]. The main tools in the proof are a fixed point theorem due to Darbo and a monotonicity measure of noncompactness.
- Fractional integral /
- quadratic integral equation /
- monotonic solutions /
- Darbo theorem /
- monotonicity measure of noncompactness
MSC: 45G10;45M99;47H09

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References

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