Study of fuzzy fractional order diffusion problem under the Mittag-Leffler Kernel Law

Abstract

Our research work is composed of designing the scheme for computation of some analytical results for fractional order fuzzy diffusion problem under Atangana-Baleanu and Caputo (    ) fractional differential operator. We have obtained the required series type solution by using the Laplace transform along with decomposition techniques. By applying the said method, we have decomposed the required whole quantity into small parts and calculate the series solution for the first few terms We have tested the develop algorithm by three different problems of one, two and three dimensions. The numerical simulations confirm that the solutions of the problems converge to their exact values at the integer-order. Further, we conclude that the fractional-order derivative yields a complete spectrum of fuzzy solutions.

Study of Fuzzy Fractional Nonlinear Equal Width Equation in the Sense of Novel Operator

“…Definition 1. Let a continuous fuzzy function of ΦðIÞ on ½0,℘ ⊂ R in the sense of Atangana-Baleanu-Caputo operator with respect to I as the following [16].…”

“…Definition 3. The "Laplace Fuzzy transformation" of Atangana-Baleanu-Caputo derivative of ΦðIÞ is defined by [16] 2 Journal of Function Spaces…”

“…The parametric form of a fuzzy number is ðκðδÞ, κðδÞÞ such that 0 ≤ δ ≤ 1; the conditions are as follows [16]:…”

“…The Atangana-Baleanu-Caputo derivative [10], a fractional nonsingular derivative proposed by Atangana, Baleanu, and Caputo, has recently gained prominence among scholars [11,12]. Using fuzzy derivatives to analyze fractional differential equations under the Atangana-Baleanu-Caputo derivative can yield a lot of exciting outcomes and open up new avenues for younger scholars [13][14][15][16].…”

Fuzzy fractional hybrid differential equations

“…The differential equations involving Riemann-Liouville differential operators of fractional order 0 < q < 1 are very important in modeling several physical phenomena [3,8,9,11,12,22] and therefore seem to deserve an independent study of their theory parallel to the well-known theory of ordinary differential equations.…”