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New generalizations for Gronwall type inequalities involving a $ \psi $-fractional operator and their applications

  • Received: 02 January 2021 Accepted: 22 February 2021 Published: 09 March 2021
  • MSC : 26A24, 26A33, 26D10, 34A08, 34A12, 34D20, 35A23

  • In this paper, we provide new generalizations for the Gronwall's inequality in terms of a $ \psi $-fractional operator. The new forms of Gronwall's inequality are obtained within a general platform that includes several existing results as particular cases. To apply our results and examine their validity, we prove the existence and uniqueness of solutions for $ \psi $-fractional initial value problem. Further, the Ulam-Hyers stability of solutions for $ \psi $-fractional differential equations is discussed. For the sake of illustrating the proposed results, we give some particular examples.

    Citation: Jehad Alzabut, Yassine Adjabi, Weerawat Sudsutad, Mutti-Ur Rehman. New generalizations for Gronwall type inequalities involving a $ \psi $-fractional operator and their applications[J]. AIMS Mathematics, 2021, 6(5): 5053-5077. doi: 10.3934/math.2021299

    Related Papers:

  • In this paper, we provide new generalizations for the Gronwall's inequality in terms of a $ \psi $-fractional operator. The new forms of Gronwall's inequality are obtained within a general platform that includes several existing results as particular cases. To apply our results and examine their validity, we prove the existence and uniqueness of solutions for $ \psi $-fractional initial value problem. Further, the Ulam-Hyers stability of solutions for $ \psi $-fractional differential equations is discussed. For the sake of illustrating the proposed results, we give some particular examples.



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