A Caputo-Type Fractional Derivative of a Function with Respect to Power Functions and Solutions to Non-Local Problems of Fractional Differential Equations

Zhengzhi Lu ()
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Zhengzhi Lu: Department of Mathematics, East China Normal University, Shanghai 200241, China

Mathematics, 2025, vol. 13, issue 22, 1-16

Abstract: This paper investigates the uniform continuity and strong continuity of the semigroups of the fractional integral operators of power functions. Using the Krasnoselskii’s fixed-point theorem, we have studied the non-local problem related to fractional differential equations involving power functions with multi-point integral boundary conditions and obtain the existence of the solution.

Keywords: fractional calculus; fractional differential equations; non-local conditions; strongly continuous semigroup; Krasnoselskii’s fixed-point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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