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BVP with a Load in the Form of a Fractional Integral

Author

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  • Minzilya Kosmakova
  • Danna Akhmanova
  • Kamila Izhanova
  • Kareem T. Elgindy

Abstract

A boundary value problem for a nonhomogeneous heat equation with a load in the form of a fractional Riemann–Liouville integral of an order β∈0,1 is considered. By inverting the differential part, the problem is reduced to an integral equation with a kernel with a special function. The special function is presented as a generalized hypergeometric function. The limiting cases of the order β of the fractional derivative are studied: it is shown that the interval for changing the order of the fractional derivative can be expanded to integer values β∈0,1. The results of the study remain unchanged. The kernel of the integral equation is estimated. Conditions for the solvability of the integral equation are obtained.

Suggested Citation

  • Minzilya Kosmakova & Danna Akhmanova & Kamila Izhanova & Kareem T. Elgindy, 2024. "BVP with a Load in the Form of a Fractional Integral," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2024, pages 1-12, May.
    • Handle: RePEc:hin:jijmms:7034103
    DOI: 10.1155/2024/7034103
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