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This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…

Classical Analysis and ODEs · Mathematics 2017-09-29 D. B. Dhaigude , Sandeep P. Bhairat

The Cauchy-type problem for a nonlinear differential equation involving Hilfer fractional derivative is considered. We prove existence, uniqueness and continuous dependence of a solution for Cauchy-type problem using successive…

Classical Analysis and ODEs · Mathematics 2017-04-10 D. B. Dhaigude , Sandeep P. Bhairat

In this article, a new definition of fractional Hilfer difference operator is introduced. Definition based properties are developed and utilized to construct fixed point operator for fractional order Hilfer difference equations with initial…

General Mathematics · Mathematics 2020-03-17 Syed Sabyel Haider , Mujeeb ur Rehman , Thabet Abdeljawad

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…

Classical Analysis and ODEs · Mathematics 2019-05-22 J. Vanterler da C. Sousa , Kishor D. Kucche , E. Capelas de Oliveira

In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions…

Classical Analysis and ODEs · Mathematics 2019-08-27 Pallavi U. Shikhare , Kishor D. Kucche , J. Vanterler da C. Sousa

This paper deals with the local existence and uniqueness results for the solution of fractional differential equations with Hilfer-Hadamrd fractional derivative. Using Picard's approximations and generalizing the restrictive conditions…

Classical Analysis and ODEs · Mathematics 2017-06-02 D B Dhaigude , Sandeep P Bhairat

The aim of this paper is to obtain the existence of unique solution to nonlinear Cauchy-type problem. We consider the implicit nonlinear Cauchy-type problem with $\psi$-Hilfer fractional derivative. The Banach fixed point theorem is used to…

General Mathematics · Mathematics 2019-10-14 Mohammed S Abdo , S K Panchal , Sandeep P Bhairat

In this paper, we present a study on the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the solution of the fractional functional differential equation using the Banach fixed point theorem.

Classical Analysis and ODEs · Mathematics 2018-07-18 J. Vanterler da C. Sousa , E. Capelas de Oliveira , F. G. Rodrigues

In this paper, we will develop a definition of mild solution for impulsive fractional differential equation of order $\alpha\in (1,2)$ with the help of solution operator and study the existence results of mild solution for impulsive…

Classical Analysis and ODEs · Mathematics 2021-09-08 G. R. Gautam , A. Dwivedi , G. Rani

The well established monotone iterative technique that is used to study the existence and uniqueness of fractional impulsive system is extended to Hilfer fractional order in this paper. The results are derived by using the method of upper…

Optimization and Control · Mathematics 2020-11-24 Divya Raghavan , Sukavanam Nagarajan

This paper deals with the existence and uniqueness of solution for a coupled system of Hilfer fractional Langevin equation with non local integral boundary value conditions. The novelty of this work is that it is more general than the works…

Analysis of PDEs · Mathematics 2022-06-16 Khalid Hilal , Ahmed Kajouni , Hamid Lmou

In this paper, using the Riemann-Liouville fractional integral with respect to another function and the $\psi-$Hilfer fractional derivative, we propose a fractional Volterra integral equation and the fractional Volterra integro-differential…

Classical Analysis and ODEs · Mathematics 2019-05-22 J. Vanterler da C. Sousa , E. Capelas de Oliveira

We consider the nonlinear Cauchy problem for $ \Psi $- 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…

Dynamical Systems · Mathematics 2020-06-23 Kishor D. Kucche , Ashwini D. Mali , J. Vanterler da C. Sousa

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 integer order and fractional order differential equations.…

Classical Analysis and ODEs · Mathematics 2019-08-16 J. Vanterler da C. Sousa , K. D. Kucche , E. Capelas de Oliveira

In this paper, we introduce a delayed Mittag-Leffler type function. With the help of the delayed Mittag-Leffler type functions, we give an explicit formula of solutions to linear nonhomogeneous fractional time-delay Langevin equations…

Dynamical Systems · Mathematics 2019-07-04 N. I. Mahmudov

In this paper, we consider sublinear second order differential equations with impulsive effects. Basing on the Poincar\'{e}-Bohl fixed point theorem, we first will prove the existence of harmonic solutions. The existence of subharmonic…

Classical Analysis and ODEs · Mathematics 2017-05-25 Yanmin Niu , Xiong Li

In present paper, we establish sufficient conditions for existence and stability of solutions for system of nonlinear implicit fractional differential equations. The main techniques are based on method of successive approximations. Finally,…

Classical Analysis and ODEs · Mathematics 2017-07-25 D. B. Dhaigude , Sandeep P. Bhairat

In this paper, we used some theorems of fixed point for studying the results of existence and uniqueness for Hilfer-Hadamard-Type fractional differential equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, \hbox{ on the interval } J:=(1,e]\]…

Analysis of PDEs · Mathematics 2018-03-14 Ahmad Y. A. Salamooni , D. D. Pawar

This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractional integral inequalities of Gr\"onwall--Wendroff type that…

Dynamical Systems · Mathematics 2026-02-10 Rômulo Damasclin Chaves dos Santos

The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate on the solutions, the continuous dependence of the solutions on initial conditions as well as the existence and uniqueness of…

Functional Analysis · Mathematics 2021-09-01 Choukri Derbazi , Qasem M. Al-Mdallal , Fahd Jarad , Zidane Baitiche