Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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MONOTONE METHOD FOR NONLINEAR HILFER FRACTIONAL REACTION-DIFFUSION EQUATIONS

  • Pandurang D. Kundgar (Department of PG Studies and Research in Mathematics, Shrikrishana Mahavidyalaya) ;
  • Jagdish A. Nanware (Department of PG Studies and Research in Mathematics, Shrikrishana Mahavidyalaya) ;
  • Gunvant A. Birajdar (Department of Mathematics, Institute of Chemical Technology)
  • Received : 2023.07.01
  • Accepted : 2024.04.29
  • Published : 2024.09.15
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Abstract

In this paper, we developed the existence and uniqueness results by monotone method for non-linear fractional reaction-diffusion equation together with initial and boundary conditions. In this text the Hilfer fractional derivative is used to denote the time fractional derivative. The employment of monotone method generates two sequences of minimal and maximal solutions which converges to lower and upper solutions respectively.

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References

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