Mishra, Lakshmi NarayanMishra, Vishnu NarayanBaleanu, DumitruPathak, Vijai Kumar2024-04-302025-09-182024-04-302025-09-182022Pathak, Vijai Kumar;...et.al. (2022). "On the Solvability of Mixed-Type Fractional-Order Non-Linear Functional Integral Equations in the Banach Space C(I)", Fractal and Fractional, Vol.6, No.12.2504-3110https://doi.org/10.3390/fractalfract6120744https://hdl.handle.net/20.500.12416/12452Mishra, Lakshmi Narayan/0000-0001-7774-7290; Pathak, Vijai Kumar/0000-0003-2477-6666; Mishra, Vishnu Narayan/0000-0002-2159-7710This paper is concerned with the existence of the solution to mixed-type non-linear fractional functional integral equations involving generalized proportional (kappa,phi)-Riemann-Liouville along with Erdelyi-Kober fractional operators on a Banach space C([1,T]) arising in biological population dynamics. The key findings of the article are based on theoretical concepts pertaining to the fractional calculus and the Hausdorff measure of non-compactness (MNC). To obtain this goal, we employ Darbo's fixed-point theorem (DFPT) in the Banach space. In addition, we provide two numerical examples to demonstrate the applicability of our findings to the theory of fractional integral equations.eninfo:eu-repo/semantics/openAccessMeasure Of Non-CompactnessFunctional Integral EquationsDarbo'S Fixed-Point TheoremFractional OperatorsBanach SpaceArticle10.3390/fractalfract61207442-s2.0-85144700445