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Differential equation systems matrix1/29/2024 ALmostafa et al., in, introduced the Aboodh and Double Aboodh transform methods to obtain the solution of PIDEs. Abdou and Elsayed, in, studied the existence of a unique solution of the fractional IDEs in Hilbert space. Abdou et al., in, applied the Adomian decomposition method for solving fractional IDEs. Al-Bugami in, applied the Toeplitz matrix and product Nystrom methods for solving two-dimensional FIDEs with singular kernels. Abdel-Aty et al., in, used the optimal axillary function method for solving FIDEs. Pandey, in, introduced the finite difference strategy to obtain the solution of Fredholm integro-differential Equations (FIDEs). Ahmed and Elzaki, in, studied the solution of IDEs by difference numerical methods. Behzadi, in, used some iterative techniques for solving Volterra-Fredholm integro-differential equations (VFIDEs). Rivaz et al., in, used Chebyshev polynomials to obtain the solution of IDEs. Mirzaee et al., in, applied Bernstein polynomials for solving PIDEs. Khajehnasiri, in, presented triangular function to obtain the solution of two-dimensional IDEs. Hamoud et al., in, studied the numerical solution of IDEs by Adomian decomposition method. Hussain et al., in, applied the variational iteration method to solve two-dimensional partial integro-differential equations (PIDEs). Tari and Shahmorad, in, introduced differential transform method for solving system of IDEs. Aghazadeh and Khajehnasiri in, used block-pulse functions for solving two-dimensional IDEs. ![]() Since these equations are difficult to solve analytically, there are many different semi-analytical approaches and numerical approaches for solving integro-differential Equations (IDEs). ![]() In these types of equations, it is not possible to obtain a single solution, but rather several solutions, the best of which can be chosen. ![]() The importance of these integro-differential equations increases, in particular if they are associated with delay. Many important problems in various sciences, such as engineering, physics, and biology, have been reduced to integral and integro-differential equations in general.
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