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Solution estimates to Caputo proportional fractional derivative delay integro-differential equations

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this article, a class of scalar generalized Caputo proportional fractional derivative delay integro-differential equations (CPFrDIDEs) with multiple non-linear kernels and multiple time delays is considered. Fundamental qualitative behaviors of the solutions such as stability, asymptotic stability, exponential stability, and boundedness of solutions are investigated. The technique used in the proofs depend upon the modified Lyapunov–Razumikhin method (LRM). As numerical applications of the novel results of this article, four examples are constructed to demonstrate that the results are valid and applicable. The outcomes of this article allow novel contributions to qualitative theory of FrDIDEs.

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Acknowledgements

The authors would like to thank the anonymous referees and the handling Editor for many useful comments and suggestions, leading to a substantial improvement of the presentation of this article.

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  1. Department of Computer, Baskale Vocational School, Van Yuzuncu Yil University, 65080, Van, Turkey

    Osman Tunç

  2. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, 65080, Van, Turkey

    Cemil Tunç

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Tunç, O., Tunç, C. Solution estimates to Caputo proportional fractional derivative delay integro-differential equations. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 12 (2023). https://doi.org/10.1007/s13398-022-01345-y

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