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

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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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Authors and Affiliations

  1. Department of Mathematics and Scientific Computing, National Institute of Technology, Hamirpur, 177005, India

    Kanika Dhawan & Ramesh Kumar Vats

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, 632014, India

    V. Vijayakumar

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  1. Kanika Dhawan
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  2. Ramesh Kumar Vats
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  3. V. Vijayakumar
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Dhawan, K., Vats, R.K. & Vijayakumar, V. Analysis of Neutral Fractional Differential Equation via the Method of Upper and Lower Solution. Qual. Theory Dyn. Syst. 22, 93 (2023). https://doi.org/10.1007/s12346-023-00795-y

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