Solving Fractional Integro-Differential Equation of Volterra type with time Delay Using the Sawi Transform

This study presents the application of the Sawi transform method to solve fractional integro-differential equation of Volterra type with time delay. The work derives the Sawi transform of the delay component in fractional integro-differential equations of Volterra type, employing the definition of Caputo fractional derivatives. Fundamental transformation formulas are established, enabling the systematic treatment of equations with difference kernels and delay terms. The proposed method provides exact analytic solutions for several illustrative examples, demonstrating its effectiveness and accuracy. Compared with traditional approaches, the Sawi transform strategy simplifies the handling of delay functions and fractional operators while preserving analytical tractability. The results confirm that the Sawi transform is a powerful and reliable tool for addressing classes of fractional integro-differential equations with constant multi-time delays. This approach may be further extended to other forms of fractional models and systems with distributed or variable delays, highlighting its potential for broader applications in applied mathematics and engineering.