Singular 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.

Fuzzy Local Fractional Differential Equations

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

Picard’s Iterative Method for Singular Fractional Differential Equations

Fractional differential equations have gained considerable importance due to their applications in various fields, such as physics, mechanics, chemistry, engineering, etc. It has been found that the differential equations involving fractional derivatives are more realistic and practical to describe many phenomena in nature[1–3]. We also refer the reader to some other works [4–7] on the fraction...

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...