Improved predictor–corrector method for solving fuzzy initial value problems

Fuzzy functional integro-differential equations under generalized H-differentiability

“…The approach based on H-derivative has the disadvantage that it leads to solutions which have an increasing length of their support. For some references on fuzzy equations and applications of fuzzy dynamics, we cite [3,11,12,20,32,33,43,44,54] and other recent works such as the study of some topological properties and structure of the solutions to the Cauchy problem for fuzzy differential systems (see [25,55]). Integrodifferential equations are encountered in many areas of science, where it is necessary to take into account aftereffect or delay (for example, in control theory, biology, ecology, medicine, et al [31,36,45]).…”

“…Also, as a very important generalization and development related to the subject of the present paper is in the field of fuzzy sets, i.e., fuzzy calculus and fuzzy differential equations under generalized Hukuhara derivative. Recently, several works as e.g., [5][6][7][8][9][10][11][12][13][14][15], [18][19][20], [2,23,29,30,42], [38][39][40], [48][49][50][51].…”

Fourth Order Diagonally Implicit Multistep Block Method for Solving Fuzzy Differential Equations

“…Ghazanfari and Shakerami [12] present the extended RK-like formulae to increase the accuracy of the solutions. Meanwhile, Allahviranloo et al (see [13], [14], [15]) use predictor-corrector method for solving FDEs by considering the Adams methods. Mehrkanoon et al [16] and Zawawi et al [17] propose block methods to solve FDEs.…”

Piecewise Approximation Method for Nth-order Fuzzy Differential Equations

“…The concept of fuzzy derivative was first introduced by Chang and Zadeh in [10], it was followed up by Dubois and Prade [11], Puri and Ralescu [20] and Goetschel and Voxman [13]. The fuzzy differential equations were rigorously treated by Kaleva [14], Sikkala [21], Kloden [17] and Menda [19].The numerical methods for solving fuzzy differential equations are introduced in [1,2,12,3,4,5] and for higher order have been studied in [9,7,6]. In this paper a new numerical method based on interpolation of fuzzy determined values is presented.…”