Necessary And Sufficient Condition For The Existence Of Solutions To Two-Point Boundary Value Problem Of Fuzzy Linear Multi-Term Fractional Differential Equations

The respected Comrade Kim Jong Un said:

"The basic sciences are the cornerstone of a sci-tech power. A high level of basic sciences enables a country's science and technology to make steady progress on a solid foundation."

We have studied the necessary and sufficient condition for the existence of solutions to two-point boundary value problem of fuzzy linear multi-term fractional differential equations.

Many of practical problems are modeled by fuzzy differential equations (FDEs), due to the uncertainty about the behavior of a system. FDEs are very important both in theory and application, such as population models, electrochemistry, problems of viscoelasticity and modeling hydraulics. So, many researchers have recently focused on the fuzzy fractional differential equations.

In Faculty of Mathematics, Kim Il Sung University, the research conducted on necessary and sufficient condition for the existence of solutions to two-point boundary value problem of fuzzy linear multi-term fractional differential equations and a series of new results obtained.

We've obtained the cut problem with inequality constraints corresponding to the fuzzy two-point boundary value problem and presented the necessary and sufficient condition for the fuzzy value function constructed from this cut problem to be the solution to the proposed problem. Also the solution expression of two-point boundary value problem for FFDEs with constant coefficients is presented by using the multivariate Mittag–Leffler function.

For more details, see our paper "Necessary and sufficient condition for the existence of solutions to two-point boundary value problem of fuzzy linear multi-term fractional differential equations" (https://doi.org/10.1007/10.1007/s00500-022-07639-y) in the Journal "Soft Computing".