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Existence of Absolutely Continuous Measure Torus Diffeomorphism

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Existence of mild solutions for multi-term time fractional measure differential equations

The Journal of Analysis volume 30,pages 1609–1623 (2022)Cite this article

Abstract

This paper focuses on a class of multi-term time-fractional measure differential equations involving nonlocal conditions. A set of sufficient conditions for the existence of mild solutions is provided. Utilizing \((\beta ,\gamma _{k})\)-resolvent family in the sense of Pardo and Lizama, measure functional (Henstock–Lebesgue–Stieltjes integral) and Schauder's fixed point theorem, we prove the existence of mild solutions. Finally, an illustrated example is presented.

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Authors and Affiliations

  1. Laboratoire d'Analyse Numérique et Informatique, Département de Mathématiques, Université Gaston Berger de Saint-Louis,  UFR SAT, B. P. 234, Saint-Louis, Senegal

    Amadou Diop

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Correspondence to Amadou Diop.

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Communicated by Samy Ponnusamy.

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Diop, A. Existence of mild solutions for multi-term time fractional measure differential equations. J Anal 30, 1609–1623 (2022). https://doi.org/10.1007/s41478-022-00420-2

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  • DOI : https://doi.org/10.1007/s41478-022-00420-2

Keywords

  • Regulated functions
  • Henstock–Lebesgue–Stieltjes integral
  • Fractional calculus
  • Generalized semigroup theory
  • Multi-term time-fractional
  • Fixed point theory

Mathematics Subject Classification

  • 34G20
  • 34K37
  • 39A99
  • 46G99

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