On the nonlinear (k,Ψ)-Hilfer fractional differential equations

Kishor D. Kucche and Ashwini D. Mali

Chaos, Solitons & Fractals, 2021, vol. 152, issue C

Abstract: In the current paper, we present the most generalized variant of the Hilfer derivative so-called (k,Ψ)-Hilfer fractional derivative operator. The (k,Ψ)-Riemann-Liouville and (k,Ψ)-Caputo fractional derivatives are obtained as a special case of (k,Ψ)-Hilfer fractional derivative. We demonstrate a few properties of (k,Ψ)-Riemann-Liouville fractional integral and derivative that expected to build up the calculus of (k,Ψ)-Hilfer fractional derivative operator. We present some significant outcomes about (k,Ψ)-Hilfer fractional derivative operator that require to derive the equivalent fractional integral equation to nonlinear (k,Ψ)-Hilfer fractional differential equation. We prove the existence and uniqueness for the solution of nonlinear (k,Ψ)-Hilfer fractional differential equation. In the conclusion section, we list the various k-fractional derivatives that are specific cases of (k,Ψ)-Hilfer fractional derivative.

Keywords: Fractional calculus; (k,Ψ)-Fractional integral; (k,Ψ)-Fractional derivative; (k,Ψ)-Fractional differential equations; Existence and uniqueness; Initial value problem (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921006895

DOI: 10.1016/j.chaos.2021.111335

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