A NEW ITERATIVE APPROACH FOR SOLVING FRACTAL-FRACTIONAL SYSTEMS OF DIFFERENTIAL EQUATIONS

Abstract

This paper presents a new iterative technique for solving fractalfractional
differential equations (FFDEs) with different kernel functions, such
as power-law, exponential and Mittag-Leffler, which are commonly used in
mathematics and physics. Bhalekar and Gejji’s method solves ordinary and
partial fractal-fractional differential equations (ODEs and PDEs). Special algorithms
are designed to make the methods accurate and efficient. These
algorithms are implemented on FFDE systems and verified by error analysis
and plots illustrating the fractal nature of the solutions. The findings show
that the proposed algorithms are stable, reliable, and efficient and can be used
to solve a broad variety of FFDE problems in science and engineering.