arXiv subjects

Kishor D. Kucche

Publications and source records attributed to Kishor D. Kucche.

21 records · Page 2Linked to original sources

arXiv2018

On the Ulam-Hyers stabilities of Ψ-Hilfer fractional differential equation by means of abstract Volterra operator

In this paper, we consider the new class of the fractional differential equation involving the abstract Volterra operator in the Banach space and investigate existence, uniqueness and stabilities of Ulam--Hyers on the compact interval $Δ=[a,b]$ and on the infinite interval $I=[a,\infty )$. Our analysis is based on the application of the Banach fixed point theorem and the Gronwall inequality involving generalized $Ψ$-fractional integral. At last, we performed out an application to elucidate the outcomes got.

math.CA↗

arXiv2018

On the Nonlinear $Ψ$-Hilfer Fractional Differential Equations

We consider the nonlinear Cauchy problem for $ Ψ$- Hilfer fractional differential equations and investigate the existence, interval of existence and uniqueness of solution in the weighted space of functions. The continuous dependence of solutions on initial conditions is proved via Weissinger fixed point theorem. Picard's successive approximation method has been developed to solve nonlinear Cauchy problem for differential equations with $ Ψ$- Hilfer fractional derivative and an estimation have been obtained for the error bound. Further, by Picard's successive approximation, we derive the representation formula for the solution of linear Cauchy problem for $ Ψ$-Hilfer fractional differential equation with constant coefficient and variable coefficient in terms of Mittag-Leffler function and Generalized (Kilbas-Saigo) Mittag-Leffler function.

math.DS↗

arXiv2018

Stability of $ψ$-Hilfer Impulsive Fractional Differential Equations

In this paper, we investigate the sufficient conditions for existence and uniqueness of solutions and δ-Ulam-Hyers-Rassias stability of an impulsive fractional differential equation involving $ψ$-Hilfer fractional derivative. Fixed point approach is used to obtain our main results.

math.CA↗