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A nonlinear boundary value problem for fractional differential equation with a derivative of Riemann-Liouville type is studied. The order of the fractional derivative is not a constant but a function depending on time variable with the range (1, 2). Equivalent integral form of the solution of the given problem is obtained. Based on this presentation we construct a sequence of functions which is convergent on the considered finite interval. The limit function is a solution of the studied nonlinear boundary value problem. The results obtained are supported by an example.

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Existence for a Nonlinear Boundary Value Problem for Riemann-Liouville Fractional Differential Equations of Variable Order

  • 会议论文

  • 发表日期：

    2025年

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  • Snezhana Hristova,
  • Mohammed Said Souid

摘要

A nonlinear boundary value problem for fractional differential equation with a derivative of Riemann-Liouville type is studied. The order of the fractional derivative is not a constant but a function depending on time variable with the range (1, 2). Equivalent integral form of the solution of the given problem is obtained. Based on this presentation we construct a sequence of functions which is convergent on the considered finite interval. The limit function is a solution of the studied nonlinear boundary value problem. The results obtained are supported by an example.