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An investigation into the characteristics of VFIDEs with delay: solvability criteria, Ulam–Hyers–Rassias and Ulam–Hyers stability

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Abstract

This article mainly focuses on studying a class of novel nonlinear Volterra-Fredholm-type integro-differential equations(VFIDE) with delay. The primary purpose of the study is to obtain results concerning Ulam–Hyers–Rassias Stability and Ulam–Hyers Stability. Additionally, the article establishes the existence of unique solutions for the considered type VFIDE. Applying the Banach contraction mapping principle without imposing strict assumptions enhances the study’s suitability for qualitative analysis. Two examples are presented to validate the proposed developments and the outcomes are visually represented through graphical illustrations.

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Abbreviations

IDE:

Integro-differential equation

VFIDE:

Volterra freedholm integro-differential equation

C(A, B):

Space of all continuous functions from A to B

\(C^1(A,B)\) :

Space of all continuously differentiable functions from A to B

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Funding

The authors affirm that this manuscript was not prepared with the help of any money, grants, or other resources.

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Author notes

  1. Mausumi Sen, R. Murugan, Nimai Sarkar and Damini Gupta have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Silchar, Silchar, 788010, Assam, India

    Bapan Ali Miah, Mausumi Sen & Damini Gupta

  2. Department of Electronics and Communications Engineering, National Institute of Technology Silchar, Silchar, 788010, Assam, India

    R. Murugan

  3. School of advanced Sciences, VIT-AP University, Amaravati, 522237, Andhra Pradesh, India

    Nimai Sarkar

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  1. Bapan Ali Miah
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  2. Mausumi Sen
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  4. Nimai Sarkar
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  5. Damini Gupta
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For the creation of the current paper, each author made an equal contribution.

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Correspondence to Bapan Ali Miah.

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Miah, B.A., Sen, M., Murugan, R. et al. An investigation into the characteristics of VFIDEs with delay: solvability criteria, Ulam–Hyers–Rassias and Ulam–Hyers stability. J Anal (2024). https://doi.org/10.1007/s41478-024-00767-8

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  • DOI: https://doi.org/10.1007/s41478-024-00767-8

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