Work

Approximation of inverse problems for fractional differential equations in abstract spaces

Year: 2025

Type: article

Abstract: This article focuses on approximating a fractional-order inverse problem (IP) for an abstract differential equation in a Hilbert space. The main tools to find out the results are fixed-point methods, the α -resolvent family, and optimal control (OC) theory. We have defined an optimal control problem corresponding to the original inverse problem, and then by using an approximate optimal control problem, we have proved that the sequence of solutions to this approximate optimal control problem will converge to the solution of our original inverse problem. Furthermore, the fractional Crank–Nicolson scheme and a matrix optimization algorithm are utilized to derive approximation results, ensuring the convergence of the proposed numerical method. Finally, an example is presented to illustrate and validate the theoretical findings.

Source: Alexandria Engineering Journal

DOI: 10.1016/j.aej.2025.02.079

Authors: Santosh Ruhil, Muslim Malik, Kottakkaran Sooppy Nisar, Fahad Sameer Al Shammari

Institutions: Indian Institute of Technology Mandi, Prince Sattam Bin Abdulaziz University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,900

Funder: Prince Sattam bin Abdulaziz University