Turkish Journal of Mathematics
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.
DOI
10.55730/1300-0098.3507
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, M, DOMOSHNITSKY, A, PADHI, S, & SRIVASTAVA, S. N (2024). Existence of solutions by coincidence degree theory for Hadamard fractionaldifferential equations at resonance. Turkish Journal of Mathematics 48 (2): 296-306. https://doi.org/10.55730/1300-0098.3507
