Numerical solution of some fractional integro-differential equations using Shehu transform and Laguerre polynomials | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 16, Issue 2, 2025, Page 1-26 PDF (530.49 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2025.353755.1157 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
AKSHAYKUMAR L DONGARDIVE  1; JAGDISH A NANAWARE 2
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| 1Department of Mathematics, Shankarrao Patil Mahavidyalaya, Bhoom , Dharashiv, Maharashtra, 413504,India | ||||
| 2Dept. of Mathematics,Shrikrishna Mahavidyalaya, Gunjoti, Dist.Dharashiv, Maharashtra, 413606, India | ||||
| Abstract | ||||
| In this paper, we present a numerical method for obtaining approximate solutions to linear fractional Fredholm and Volterra-Fredholm integro-differential equations with separable kernels. The proposed method utilizes the Shehu integral transform in combination with Laguerre polynomials. Specifically, the unknown solution is expressed as a truncated series of Laguerre polynomials. By applying the Shehu transform and using collocation points, the integro-differential equation is converted into a system of linear algebraic equations. This system is then solved using MATLAB. The fractional derivative is considered in the Caputo sense. To demonstrate the effectiveness of the method, six examples are provided: four related to fractional Fredholm integro-differential equations, one for a Volterra-Fredholm type equation, and one for a Volterra type equation. The performance of the method is evaluated by calculating the absolute errors between the approximate and exact solutions. The numerical results confirm that the proposed approach yields accurate approximations and is suitable for solving such fractional integro-differential equations. | ||||
| Keywords | ||||
| Fractional integro-differential equations (FIDEs); Shehu transform; Laguerre polynomials; Caputo derivative | ||||
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