Studies on Fuzzy Fractional Differential Equations

Abstract

One of the most recent and significant developments in the field of fuzzy mathematics is newlinea fuzzy fractional differential equations. It has a wide range of applications, since many newlinereal-world problems in science, engineering and optimization can be transformed into newlinefractional order problems with uncertainty. This research mainly focuses on exploring newlinenew techniques to solve fuzzy fractional delay differential equations, system of fuzzy newlinefractional differential equations, fuzzy fractional boundary value problems and fuzzy newlineHilfer fractional differential equations. newlineA novel procedure to solve the fuzzy fractional delay differential equations with triangular newlinefuzzy source functions and initial conditions has been discussed. The derived newlinesolution is represented by fuzzy collection of real functions. In addition, fractional dynamics newlineis greatly influenced by the matrix Mittag-Leffler functions. A generalization newlineof the matrix exponential function is the matrix Mittag-Leffler function. The solutions newlineof the system of fuzzy fractional differential equations is obtained in the form of matrix newlineMittag-Leffler function. The Jordan canonical approach and minimal polynomial newlineapproach is utilized to find this function. The numerical results are compared with the newlineeigenvalue-eigenvector approach for the system of fuzzy fractional differential equations. newlineFurther, the solution to the non-homogeneous system of fuzzy fractional differential newlineequations is obtained by utilizing fuzzy functions. Consequently, the solution newlineof fuzzy fractional boundary value problem is investigated using fuzzy functions. The newlinesolution to this problem is expressed in terms of a fuzzy collection of real functions. newlineFractional calculus has introduced various derivative formulas, including Riemann- newlineLiouville, Caputo and Hilfer. Finally, expanding on the theory of fractional differential newlineequations, the Adomian decomposition procedure for obtaining the solution of fuzzy newlineHilfer fractional differential equations is discussed. Through numerical examples, the newlineefficacy and accura