An Application of Artificial Neural Networks for Solving Fractional Higher-order Linear Integro-differential Equations - Allahviranloo, T.; Jafarian, A.; Saneifard, R.; Ghalami, N.; Nia, S. Measoomy; Kiani, F.; Gamiz, U. Fernandez; Noeiaghdam, S. (Springer Nature, 2023)
This ongoing work is vehemently dedicated to the investigation of a class of ordinary linear Volterra type integro-differential equations with fractional order in numerical mode. By replacing the unknown function by an appropriate multilayered feed-forward type neural structure, the fractional problem of such initial value is changed into a course of non-linear minimization equations, to some extent. Put differently, interest was sparked in structuring an optimized iterative first-order algorithm to estimate solutions for the origin fractional problem. On top of that, some computer simulation models exemplify the preciseness and well-functioning of the indicated iterative technique. The outstanding accomplished numerical outcomes conveniently reflect the productivity and competency of artificial neural network methods compared to customary approaches.
Keywords: Higher-order Linear Integro-differential Equation; Artificial Neural Network Approach; Caputo Fractional Derivative; Learning Algorithm; Cost Function