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Peer-reviewedCC BY 4.0Fractal and Fractional

An Initial-Value Problem for an Ordinary Differential Equation Involving Multi-Term Time-Fractional Derivatives with Relaxation Factors

  • Fikret Gölgeleyen1
  • Seher Seda Sarıköse Bayram2
  • Masahiro Yamamoto1,3
  1. 1Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, Zonguldak 67100, Türkiye
  2. 2Graduate School of Natural and Applied Sciences, Zonguldak Bülent Ecevit University, Zonguldak 67100, Türkiye
  3. 3Department of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914, Japan
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Abstract

In this article, we consider an initial-value problem for a linear ordinary differential equation with multi-term time fractional derivatives with relaxation factors, which make the current work differently from existing studies in the literature. We establish the unique existence and the stability of the solution to the problem within the framework of suitable Sobolev spaces. Moreover, we present an improved regularity result for the solution. Our treatment is based on the operator theory in Sobolev spaces.

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Cite

BibTeXRIS
BibTeX
@article{golgeleyen2026initialvalue,
  title = {{An Initial-Value Problem for an Ordinary Differential Equation Involving Multi-Term Time-Fractional Derivatives with Relaxation Factors}},
  author = {Fikret Gölgeleyen and Seher Seda Sarıköse Bayram and Masahiro Yamamoto},
  journal = {Fractal and Fractional},
  year = {2026},
  month = nov,
  doi = {10.3390/fractalfract10110773},
  url = {https://www.mdpi.com/2504-3110/10/11/773},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - An Initial-Value Problem for an Ordinary Differential Equation Involving Multi-Term Time-Fractional Derivatives with Relaxation Factors
AU  - Fikret Gölgeleyen
AU  - Seher Seda Sarıköse Bayram
AU  - Masahiro Yamamoto
PY  - 2026
DA  - 2026/11/05
JO  - Fractal and Fractional
DO  - 10.3390/fractalfract10110773
UR  - https://www.mdpi.com/2504-3110/10/11/773
AB  - In this article, we consider an initial-value problem for a linear ordinary differential equation with multi-term time fractional derivatives with relaxation factors, which make the current work differently from existing studies in the literature. We establish the unique existence and the stability of the solution to the problem within the framework of suitable Sobolev spaces. Moreover, we present an improved regularity result for the solution. Our treatment is based on the operator theory in Sobolev spaces.
SN  - 2504-3110
ER  -