Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ANALYTICAL AND APPROXIMATE SOLUTIONS FOR GENERALIZED FRACTIONAL QUADRATIC INTEGRAL EQUATION

  • Abood, Basim N. (Department of Mathematics, College of Education of Pure Science University of Wasit) ;
  • Redhwan, Saleh S. (Babasaheb Ambedkar Marathwada University) ;
  • Abdo, Mohammed S. (Department of Mathematics, Hodeidah University)
  • Received : 2020.10.13
  • Accepted : 2021.02.07
  • Published : 2021.09.15
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Abstract

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.

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