arXiv subjects

Jyoti P. Kharade

Publications and source records attributed to Jyoti P. Kharade.

4 recordsLinked to original sources

arXiv2019

On the Impulsive Implicit $Ψ$--Hilfer Fractional Differential Equations with Delay

In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit $Ψ$--Hilfer fractional differential equations with time delay. It is demonstrated that the Ulam--Hyers and generalized Ulam--Hyers stability are the specific cases of Ulam--Hyers--Mittag--Leffler stability. Extended version of Gronwall inequality, abstract Gronwall lemma and Picard operator theory are the primary devices in our investigation. We give an example to illustrate the obtained results.

math.DS↗

arXiv2019

Analysis of Impulsive $φ$--Hilfer Fractional Differential Equations

This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $φ$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the initial conditions, order of derivative and the functions involved in the equations. The outcomes are acquired in the space of weighted piecewise continuous functions by means of fixed point theorems and the generalized version of Gronwall inequality.

math.DS↗

arXiv2019

Global Existence and Ulam--Hyers Stability of $Ψ$--Hilfer Fractional Differential Equations

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving $Ψ$-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam--Hyers and Ulam--Hyers--Rassias stability of Cauchy--type problem is investigated via successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and uniqueness via $ε$-approximated solution. An example is provided to illustrate the results we obtained.

math.DS↗

arXiv2019

On the Nonlinear Impulsive $Ψ$--Hilfer Fractional Differential Equations

In this paper, we consider the nonlinear $Ψ$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are extended to the nonlocal $Ψ$-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we procured. Further, examples are provided in support of the results we got.

math.DS↗