Elementary Differential Equations.

Elementary and Liouvillian Solutions of Linear Differential Equations

Let L(y)= b be a linear differential equation with coefficients in a differential field k, of characteristic 0. We show that if L(y)= b has a non-zero solution Liouvillian over k, then either L(y) = 0 has a non-zero solution u such that u'/u is algebraic over k, or L(y) = b has a solution in k. If L(y) = b has a non-zero solution elementary over k, then either L(y) = 0 has a non-zero solution a...

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Solution of fuzzy differential equations

Hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎The hybrid differential equations have a wide range of applications in science and engineering‎. ‎The hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎Hybrid fuzzy differential equations (HFDEs) is considered by ...

Fuzzy Local Fractional Differential Equations

Functional Differential Equations Close to Differential Equations

when the lag function r(t) is nearly constant for large /, and has also asked for conditions on the function r under which all solutions approach zero as t—» oo. The purpose of this announcement is to initiate a study of various stability and oscillation problems for equations with perturbed lag functions, and to suggest that a modification of the familiar method of conversion to an integral eq...