135 citations · 640 across the 20 of their papers we have counts for
20 papers
On tempered fractional calculus with respect to functions and the associated fractional differential equations
Ashwini D. Mali, Kishor D. Kucche, Arran Fernandez +1
The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function. This theory…
On Coupled System of Nonlinear -Hilfer Hybrid Fractional Differential Equations
Ashwini D. Mali, Kishor D. Kucche, J. Vanterler da C. Sousa
This paper is dedicated to investigating the existence of solutions to the initial value problem (IVP) for a coupled system of -Hilfer hybrid fractional differential equations (…
On the Boundary Value Problems of Ψ -Hilfer Fractional Differential Equations
Ashwini D. Mali, Kishor D. Kucche
In the current paper, we derive the comparison results for the homogeneous and non-homogeneous linear initial value problem (IVP) for -Hilfer fractional differential equations.…
On the Nonlinear -Hilfer Hybrid Fractional Differential Equations
Kishor D. Kucche, Ashwini D. Mali
In this paper, we initially derive the equivalent fractional integral equation to -Hilfer hybrid fractional differential equations and through it, we prove the existence of a so…
On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative
Sagar T. Sutar, Kishor D. Kucche
In this paper, we develop the theory of nonlinear hybrid fractional differential equations involving Atangana--Baleanu--Caputo (ABC) fractional derivative. We construct the equival…
Implicit Fractional Differential Equations in Banach Spaces via Picard and Weakly Picard Operator Theory
Sagar T. Sutar, Kishor D. Kucche
In this paper, by employing fixed-point methods, we obtain the existence and uniqueness results for the nonlinear implicit fractional differential equations in Banach spaces. Furth…
Analysis of Nonlinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative
Kishor D. Kucche, Sagar T. Sutar
In the present paper, we determine the estimations on Atangana-Baleanu-Caputo fractional derivative at extreme points. With the assistance of the estimations obtained, we derive th…
Nonlocal Boundary Value Problem for Generalized Hilfer Implicit Fractional Differential Equations
Ashwini D. Mali, Kishor D. Kucche
In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving -Hilfer fractional derivative subject…
On the Nonlinear Impulsive Volterra-Fredholm Integrodifferential Equations
Pallavi U. Shikhare, Kishor D. Kucche, J. Vanterler da C. Sousa
In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we…
Analysis of Volterra Integrodifferential Equations with Nonlocal and Boundary Conditions via Picard Operator
Pallavi U. Shikhare, Kishor D. Kucche, J. Vanterler da C. Sousa
This article investigates the existence and uniqueness of solutions to the second order Volterra integrodifferential equations with nonlocal and boundary conditions through its int…
On the Impulsive Implicit --Hilfer Fractional Differential Equations with Delay
Jyoti P. Kharade, Kishor D. Kucche
In this paper, we investigate the existence and uniqueness of solutions and derive the Ulam--Hyers--Mittag--Leffler stability results for impulsive implicit --Hilfer fractional…
Analysis of Impulsive --Hilfer Fractional Differential Equations
Kishor D. Kucche, Jyoti P. Kharade
This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive --Hilfer fractional differential equations. Further, w…
Ulam-Hyers stabilities of mild solutions of the fractional nonlinear abstract Cauchy problem
J. Vanterler da C. Sousa, K. D. Kucche, E. Capelas de Oliveira
Since the main work on Ulam-Hyers dependable stabilities of differential equations to date, numerous significant and applicable papers have been published, both in the sense of int…
On the Nonlinear Impulsive --Hilfer Fractional Differential Equations
Kishor D. Kucche, Jyoti P. Kharade, J. Vanterler da C. Sousa
In this paper, we consider the nonlinear -Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existen…
On Impulsive Delay Integrodifferential Equations with Integral Impulses
Kishor D. Kucche, Pallavi U. Shikhare
The present research paper is devoted to investigate the existence, uniqueness of mild solutions for impulsive delay integrodifferential equations with integral impulses in Banach…
On Fractional Volterra integrodifferential equations with fractional integrable impulses
Sagar T. Sutar, Kishor D. Kucche
We consider a class of nonlinear fractional Volterra integrodifferential equation with fractional integrable impulses and investigate the existence and uniqueness results in the Bi…
On the Ulam-Hyers stabilities of Ψ-Hilfer fractional differential equation by means of abstract Volterra operator
J. Vanterler da C. Sousa, Kishor D. Kucche, E. Capelas de Oliveira
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…
On the Nonlinear -Hilfer Fractional Differential Equations
Kishor D. Kucche, Ashwini D. Mali, J. Vanterler da C. Sousa
We consider the nonlinear Cauchy problem for - Hilfer fractional differential equations and investigate the existence, interval of existence and uniqueness of solution in the w…
Global Existence and Ulam--Hyers Stability of --Hilfer Fractional Differential Equations
Kishor D. Kucche, Jyoti P. Kharade
In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving -Hilfer fractional derivative and prove the existence and uniqueness of soluti…
Stability of -Hilfer Impulsive Fractional Differential Equations
J. Vanterler da C. Sousa, Kishor D. Kucche, E. Capelas de Oliveira
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 equatio…