Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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EXISTENCE AND APPROXIMATE SOLUTION FOR THE FRACTIONAL VOLTERRA FREDHOLM INTEGRO-DIFFERENTIAL EQUATION INVOLVING ς-HILFER FRACTIONAL DERIVATIVE

  • Awad T. Alabdala (Management Department - Universite Francaise d'Egypte) ;
  • Alan jalal abdulqader (Mathematical Department, College of Education, Al-Mustansiriyah University) ;
  • Saleh S. Redhwan (School of Mathematical Sciences, Zhejiang Normal University) ;
  • Tariq A. Aljaaidi (Department of Mathematics, Hajjah University)
  • Received : 2023.03.04
  • Accepted : 2023.04.17
  • Published : 2023.12.15
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Abstract

In this paper, we are motivated to evaluate and investigate the necessary conditions for the fractional Volterra Fredholm integro-differential equation involving the ς-Hilfer fractional derivative. The given problem is converted into an equivalent fixed point problem by introducing an operator whose fixed points coincide with the solutions to the problem at hand. The existence and uniqueness results for the given problem are derived by applying Krasnoselskii and Banach fixed point theorems respectively. Furthermore, we investigate the convergence of approximated solutions to the same problem using the modified Adomian decomposition method. An example is provided to illustrate our findings.

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References

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