Fractional Integral Equations Tell Us How to Impose Initial Values in Fractional Differential Equations

Fuzzy Local Fractional Differential Equations

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.

FRACTIONAL CALCULUS : Integral and Differential Equations of Fractional Order

. . . . . . . . . . . . . . . . . . . . . . . . . p. 223

Fractional differential equations with Legendre polynomials

Legendre Wavelets for Solving Fractional Differential Equations

In this paper, we develop a framework to obtain approximate numerical solutions to ordi‌nary differential equations (ODEs) involving fractional order derivatives using Legendre wavelets approximations. The continues Legendre wavelets constructed on [0, 1] are uti‌lized as a basis in collocation method. Illustrative examples are included to demonstrate the validity and applicability of the techn...