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
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• 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.