Research article

Solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type

  • Received: 10 October 2019 Accepted: 06 December 2019 Published: 12 December 2019
  • MSC : 34N05, 34A12

  • In this paper, we consider the solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type. The expression of the solution for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is discussed based on the definition and the property of the Caputo differential operators. By the fixed point theorem in Banach algebra due to Dhage, an existence theorem for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is given under mixed Lipschitz and Carathéodory conditions. As an application, an example is presented to illustrate the main results. Our results in this paper extend and improve some well-known results. To some extent, our work fills the gap on some basic theory for the boundary value problems of fractional differential equations with mixed perturbations of the second type involving Caputo differential operator.

    Citation: Yige Zhao, Yibing Sun, Zhi Liu, Yilin Wang. Solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type[J]. AIMS Mathematics, 2020, 5(1): 557-567. doi: 10.3934/math.2020037

    Related Papers:

  • In this paper, we consider the solvability for boundary value problems of nonlinear fractional differential equations with mixed perturbations of the second type. The expression of the solution for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is discussed based on the definition and the property of the Caputo differential operators. By the fixed point theorem in Banach algebra due to Dhage, an existence theorem for the boundary value problem of nonlinear fractional differential equations with mixed perturbations of the second type is given under mixed Lipschitz and Carathéodory conditions. As an application, an example is presented to illustrate the main results. Our results in this paper extend and improve some well-known results. To some extent, our work fills the gap on some basic theory for the boundary value problems of fractional differential equations with mixed perturbations of the second type involving Caputo differential operator.


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