In this paper we establish some bounds for the solution of a Cauchy-type problem for a class of fractional differential equations with a weighted sequential fractional derivative. The bounds are based on a Bihari-type inequality and a bound on Gauss hypergeometric function.

This paper presents a general solution of hyperbolic type equation with second-order singular coefficient and to the Cauchy problem posed for this equation.

Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem.