An operator method for composite fractional partial differential equations

Huiwen Wang and Fang Li

Chaos, Solitons & Fractals, 2025, vol. 198, issue C

Abstract: A composite fractional-order partial differential equation is a type of partial differential equation that combines integer-order and fractional-order derivatives, enabling more accurate characterization of the dynamical behaviors of complex systems. We study this kind of equation, which incorporates the Caputo fractional derivatives of orders 1<α<2 and 0≤β<1 in a Banach space. Utilizing the theory of (a,k)-regularized resolvent families of bounded and linear operators, we delineate the solution pertinent to the abstract form of these equations. In addition, we establish results pertaining to the existence and uniqueness of solutions. Specifically, we obtain the existence and uniqueness of solutions for the fractional oscillation equation with initial value conditions. Furthermore, applying our results, we solve a multi-term composite abstract fractional differential equation, a Sobolev-type composite fractional differential equation, a Bagley–Torvik equation and a fractional control system.

Keywords: Composite fractional differential equation; Caputo fractional derivative; (a, k)-regularized resolvent family (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:198:y:2025:i:c:s0960077925005156

DOI: 10.1016/j.chaos.2025.116502

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