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Analysis of Neutral Fractional Differential Equation via the Method of Upper and Lower Solution

  • Kanika Dhawan [1] ; Ramesh Kumar Vats [1] ; V. Vijayakumar [2]
    1. [1] National Institute Of Technology

      National Institute Of Technology

      Japón

    2. [2] Vellore Institute of Technolog
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
  • Idioma: inglés
  • Enlaces
  • Resumen

    • This manuscript is concerned about the study of the existence of solutions for the class of nonlinear neutral Caputo-Hadamard fractional differential equations including integral terms. In order to establish the necessary conditions of solvability for the proposed problem, we apply the semi-group property of Hadamard fractional integral operator. Also, under the appropriate conditions, we demonstrate that the solution set for the proposed problem is non-empty by using Arzelá-Ascoli theorem and the method of upper and lower solutions. In contrast to the fundamental results graphical example is also presented in order to validate the findings.

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