Study of fuzzy fractional order diffusion problem under the Mittag-Leffler Kernel Law
Muhammad Arfan, Kamal Shah, Aman Ullah, Thabet Abdeljawad
Abstract
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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> <mml:mi mathvariant="italic"></mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> 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.