A computational framework for fractional integro-differential equations involving mixed integral terms

Mohapatra, Siba Prasad; Nath, Anasuya

doi:10.22124/jmm.2026.32894.2993

A computational framework for fractional integro-differential equations involving mixed integral terms

Articles in Press

Document Type : Research Article

Authors

¹ Assistant Professor, Department of Mathematics, Konark Institute of Science and Technology, Bhubaneswar, India

² Professor Department of Mathematics Utkal University Bhubaneswar, India

10.22124/jmm.2026.32894.2993

Abstract

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.

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