Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions

Abstract

The given article describes the implicit fractional dierential equation with anti-periodic boundary conditions
in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the
given problem and prove the existence and uniqueness results of such a problem using the Banach and
Krasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, the Ulam-Hyers
stability results are discussed. To show the eectiveness of the acquired results, convenient examples are
presented.

Keywords

• implicit fractional differential equation
• fractional derivative and fractional integral
• anti-periodic conditions
• fixed point theorem
• Gronwall inequality

Kaynakça

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