Investigation the boundary and initial value problems including fractional integro-differential equations with singular kernels

Document Type : Original Paper

Authors

1 Department of Industrial Engineering, Apadana Institute of Higher Education, Shiraz, Iran

2 Faculty of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

3 Faculty of Mathematics, Azarbaijan Shahid Madani University Tabriz, Iran

Abstract

In this paper, the initial and boundary value problems which includes singular fractional integro-differential equations, are investigated. The fractional derivative which is considered in this article, is the Caputo fractional derivative. The integral equations which are discussed in this paper either without any singularity or contain singular kernels that can be weak or strong. In addition to, in this paper to check and study the singularity and regularity of this type of integral equations are paid. Also, the given integral equations are in the form of initial and boundary value problems, which are discussed in terms of the number and manner of boundary conditions. Finally, some examples are provided for the accuracy and efficiency of the method.

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References

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Journal of Advanced Mathematical Modeling
Volume 11, Issue 1
April 2021
Pages 97-108

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History

  • Receive Date: 17 August 2020
  • Revise Date: 12 December 2020
  • Accept Date: 21 January 2021

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