THE UNIQUE EXISTENCE OF SOLUTION IN THE q-INTEGRABLE SPACE FOR THE NONLINEAR q-FRACTIONAL DIFFERENTIAL EQUATIONS

Tie Zhang and Yuzhong Wang
Additional contact information
Tie Zhang: Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, P. R. China
Yuzhong Wang: Department of Mathematics and the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-13

Abstract: In this paper, we study the solution theory of the nonlinear q-fractional differential equation of Caputo type cD qαy(t) = f(t,y(t)) with given initial values Dqky(0 +) = dk,k = 0, 1,…,n − 1 where α > 0 is the order, n = [α] and 0 < q < 1 is the scale index. For 0 ≤ β < α − n + 1, by assuming that function tβf(t,y) is bounded and satisfies the Lipschitz condition on variable y, we prove that this problem admits a unique solution in the q-integrable function space 𠒟q(n)(0,b) and this solution is absolutely stable in the L∞-norm. This unique existence condition allows that f(t,y) is singular at t = 0 and discontinuous for t ∈ (0,b]. Finally, a successive approximation method is presented to find out the analytic approximation solution of this problem.

Keywords: The q-Fractional Differential Equation; The q-Integrable Function Space; Unique Existence of Solution; Stability; Successive Approximation Method (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X2150050X
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x2150050x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X2150050X

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().