Existence of solutions by coincidence degree theory for Hadamard fractionaldifferential equations at resonance

Authors

MARTIN BOHNERFollow
ALEXANDER DOMOSHNITSKYFollow
Seshadev PADHIFollow
Satyam Narayan SRIVASTAVAFollow

DOI

10.55730/1300-0098.3507

Abstract

Using the coincidence degree theory of Mawhin and constructing appropriate operators, we investigate the existence of solutions to Hadamard fractional differential equations (FRDEs) at resonance { − (HDγu ) (t) = f(t, u(t)), t ∈ (1, e), u(1) = 0, u(e) = ∫ e 1 u(t)dA(t), where 1 < γ < 2, f : [1, e]×R2 → R satisfies Carathéodory conditions, ∫ e 1 u(t)dA(t) is the Riemann–Stieltjes integration, and (HDγu ) is the Hadamard fractional derivation of u of order γ . An example is included to illustrate our result.

Keywords

Fractional integral, fractional derivative, Hadamard derivative, boundary value problem, existence of solutions, coincidence degree theory

First Page

296

Last Page

306

Recommended Citation

BOHNER, MARTIN; DOMOSHNITSKY, ALEXANDER; PADHI, Seshadev; and SRIVASTAVA, Satyam Narayan (2024) "Existence of solutions by coincidence degree theory for Hadamard fractionaldifferential equations at resonance," Turkish Journal of Mathematics: Vol. 48: No. 2, Article 13. https://doi.org/10.55730/1300-0098.3507
Available at: https://journals.tubitak.gov.tr/math/vol48/iss2/13