University of Guilan Journal of Mathematical Modeling 2345-394X 2026 05 15 A computational framework for fractional integro-differential equations involving mixed integral terms 9606 10.22124/jmm.2026.32894.2993 EN Siba Prasad Mohapatra Assistant Professor, Department of Mathematics, Konark Institute of Science and Technology, Bhubaneswar, India Anasuya Nath Professor Department of Mathematics Utkal University Bhubaneswar, India Journal Article 2026 02 03 This paper proposes an efficient difference scheme for addressing Volterra integro-differential equations of fractional order with a mixed integral term. The fractional operator is taken in the Caputo sense of order \( \sigma \in (0,1) \). We start by establishing sufficient conditions for the existence of a unique solution. The differential operator is discretized using the \(L1\) method on a uniform grid, and composite trapezoidal formula is applied to approximate the mixed integral. A comprehensive convergence analysis is carried out under appropriate regularity conditions on the initial data. The findings show that the derived scheme achieves the convergence rate of \( (2 - \sigma) \). Numerical experiments are conducted to substantiate the theoretical conclusions and illustrate the effectiveness of the scheme. https://jmm.guilan.ac.ir/article_9606_237357904b677f5c3b11bde53f0eed7a.pdf