Analysis of Mild Extremal Solutions in Nonlinear Caputo-Type Fractional Delay Difference Equations

Ravi P. Agarwal and Ekaterina Madamlieva ()
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Ravi P. Agarwal: Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA
Ekaterina Madamlieva: Department of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1756 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 8, 1-27

Abstract: This study investigates extremal solutions for fractional-order delayed difference equations, utilizing the Caputo nabla operator to establish mild lower and upper approximations via discrete fractional calculus. A new approach is employed to demonstrate the uniform convergence of the sequences of lower and upper approximations within the monotone iterative scheme using the summation representation of the solutions, which serves as a discrete analogue to Volterra integral equations. This research highlights practical applications through numerical simulations in discrete bidirectional associative memory neural networks.

Keywords: Caputo-type fractional difference; nabla fractional sum; constant delay; mild upper and lower solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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