Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions

• Published in: Soft computing (Berlin, Germany) Vol. 24; no. 16; pp. 12501 - 12522
• Main Authors: Arqub, Omar Abu, Al-Smadi, Mohammed
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2020; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Calculus; Computational Intelligence; Control; Differential equations; Engineering; Fractional calculus; Fuzzy sets; Graphical representations; Hilbert space; Mathematical Logic and Foundations; Mechatronics; Methodologies and Application; Robotics; Characterization theorem; Fuzzy conformable fractional differential equation; Fuzzy conformable derivative and integral; Reproducing kernel Hilbert space method
• ISSN: 1432-7643; 1433-7479
• DOI: 10.1007/s00500-020-04687-0

The aim of this article is to propose a new definition of fuzzy fractional derivative, so-called fuzzy conformable. To this end, we discussed fuzzy conformable fractional integral softly. Meanwhile, uniqueness, existence, and other properties of solutions of certain fuzzy conformable fractional differential equations under strongly generalized differentiability are also utilized. Furthermore, all needed requirements for characterizing solutions by equivalent systems of crisp conformable fractional differential equations are debated. In this orientation, modern trend and new computational algorithm in terms of analytic and approximate conformable solutions are proposed. Finally, the reproducing kernel Hilbert space method in the conformable emotion is constructed side by side with numerical results, tabulated data, and graphical representations.