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A computational framework for fractional integro-differential equations involving mixed integral terms | ||
| Journal of Mathematical Modeling | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 25 اردیبهشت 1405 اصل مقاله (443.86 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2026.32894.2993 | ||
| نویسندگان | ||
| Siba Prasad Mohapatra* 1؛ Anasuya Nath2 | ||
| 1Assistant Professor, Department of Mathematics, Konark Institute of Science and Technology, Bhubaneswar, India | ||
| 2Professor Department of Mathematics Utkal University Bhubaneswar, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Caputo derivative؛ fractional integro-differential equation؛ L1 technique؛ trapezoidal formula؛ error estimation | ||
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