Mishra, Lakshmi NarayanMishra, Vishnu NarayanBaleanu, DumitruPaul, Supriya Kumar02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2024-05-282025-09-182024-05-282025-09-182023Paul, Supriya Kumar...et al. (2023). "Analysis of mixed type nonlinear Volterra–Fredholm integral equations involving the Erdélyi–Kober fractional operator", Journal of King Saud University - Science, Vol. 35, No. 10.1018-36472213-686Xhttps://doi.org/10.1016/j.jksus.2023.102949https://hdl.handle.net/123456789/10694Paul, Supriya Kumar/0000-0003-1040-1820; Mishra, Lakshmi Narayan/0000-0001-7774-7290This paper investigates the existence, uniqueness and stability of solutions to the nonlinear Volterra-Fredholm integral equations (NVFIE) involving the Erdelyi-Kober (E-K) fractional integral operator. We use the Leray- Schauder alternative and Banach's fixed point theorem to examine the existence and uniqueness of solutions, and we also explore Hyers-Ulam (H-U) and Hyers-Ulam-Rassias (H-U-R) stability in the space C([0, fl], R). Furthermore, three solution sets U-sigma,U-lambda, U-theta,U-1 and U-1,U-1 are constructed for sigma > 0, lambda > 0, and theta is an element of (0,1), and then we obtain local stability of the solutions with some ideal conditions and by using Schauder fixed point theorem on these three sets, respectively. Also, to achieve the goal, we choose the parameters for the NVFIE as delta is an element of (1/2, 1), p is an element of (0,1), gamma > 0. Three examples are provided to clarify the results.eninfo:eu-repo/semantics/openAccessErdelyi-Kober Fractional Integral OperatorHyers-Ulam-Rassias StabilityHyers-Ulam StabilityLocal StabilityFixed Point TheoremArticle10.1016/j.jksus.2023.1029492-s2.0-85175702618