Numerical solutions of a generalized time fractional partial integro-differential equation of Volterra type via an extended cubic B-spline technique
Year: 2026
Type: article
Abstract: In this work, we investigate numerical solutions of a generalized time-fractional partial integro-differential equation (TFPIDE) of Volterra type. The equation incorporates Caputo fractional derivatives and convolution-type integral terms, making it suitable for modeling physical processes with memory and non-local effects. To approximate the solution, we employ a temporal discretization based on the L1-2 scheme for the Caputo derivative and a composite trapezoidal rule for the integral term. Spatial discretization is carried out using the extended cubic B-spline (ECBS) collocation method, which generalizes classical cubic B-splines and provides enhanced flexibility and accuracy. Convergence analysis is established, proving that the proposed scheme achieves second-order accuracy in space and optimal error bounds in time. Several numerical examples are presented to demonstrate the efficiency, stability, and accuracy of the method.
Source: Boundary Value Problems
Authors: Ahmed Bassim, Ali Barati
Institution: Razi University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,890
OpenAlex ID: W7204142159
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