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In this paper, we are concerned with the mild solutions of Riemann-Liouville fractional differential equations with nonlocal conditions in Banach space. We use Banach contraction principle to prove the existence and uniqueness. Moreover, we…

Classical Analysis and ODEs · Mathematics 2015-07-31 Zhan-Dong Mei , Ji-Gen Peng

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 manuscript we investigate the existence and uniqueness of an impulsive fractional dynamic equation on time scales involving non-local initial condition with help of Caputo nabla derivative. The existency is based on the Scheafer's…

Analysis of PDEs · Mathematics 2022-07-05 Bikash Gogoi , Bipan Hazarika , Utpal Kumar Saha

In this work we study a generalized nonlocal thermistor problem with fractional-order Riemann-Liouville derivative. Making use of fixed-point theory, we obtain existence and uniqueness of a positive solution.

Analysis of PDEs · Mathematics 2012-11-05 Moulay Rchid Sidi Ammi , Delfim F. M. Torres

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the the pseudo-index…

Analysis of PDEs · Mathematics 2018-09-06 Vincenzo Ambrosio , Giovanni Molica Bisci

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…

Classical Analysis and ODEs · Mathematics 2024-07-16 Marc Jornet

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

This article contains a new discussion for the generalized fractional Cauchy-type problem involving Hilfer-Katugampola-type fractional derivative. We study an existence and continuation of its solution. Firstly, we establish a new theorems…

Analysis of PDEs · Mathematics 2020-02-11 Ahmad Y. A. Salamooni , D. D. Pawar

This paper is devoted to a nonlinear singular Riemann-Liouville type fractional differential equation, the local existence of whose continuous solutions under the weakest condition remained as an open problem until now. The singularity of…

General Mathematics · Mathematics 2021-11-30 Müfit Şan

Using a fixed point theorem in a proper Banach space, we prove existence and uniqueness results of positive solutions for a fractional Riemann-Liouville nonlocal thermistor problem on arbitrary nonempty closed subsets of the real numbers.

Analysis of PDEs · Mathematics 2018-06-28 Moulay Rchid Sidi Ammi , Delfim F. M. Torres

In this paper, we present some results for existence of global solutions and attractivity for mulidimensional fractional differential equations involving Riemann-Liouville derivative. First, by using a Bielecki type norm and Banach fixed…

Classical Analysis and ODEs · Mathematics 2017-09-08 H. T. Tuan , Adam Czornik , J. Nieto , M. Niezabitowski

Existence of solutions to a $\Phi$-Laplacian singular system is obtained via shifting method and variational methods. A priori estimates are furnished through De Giorgi's technique, Talenti's rearrangement argument, and exploiting the weak…

Analysis of PDEs · Mathematics 2023-06-30 Laura Gambera , Umberto Guarnotta

This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…

Analysis of PDEs · Mathematics 2020-04-22 Giovanni Molica Bisci , Dušan D. Repovš

We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asymptotically linear problem in general domains. Furthermore, we…

Analysis of PDEs · Mathematics 2022-07-25 Abdelrazek Dieb , Isabella Ianni , Alberto Saldaña

Utilising the notion of measures of non-compactness and Kamke function of order $\alpha$, we address the question of solvability of fractional differential equations in Banach spaces. In particular, we provide sufficient conditions ensuring…

Functional Analysis · Mathematics 2025-11-05 Dušan Oberta

The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions…

Optimization and Control · Mathematics 2021-12-15 Lavina Sahijwani , N. Sukavanam , Abdul Haq

This paper is devoted to study the existence of a solution to Hilfer fractional differential equation with nonlocal boundary condition. We use the equivalent integral equation to study the considered Hilfer differential problem with…

General Mathematics · Mathematics 2019-10-01 Hanan A. Wahash , Mohammed S. Abdo , Satish K. Panchal , Sandeep P. Bhairat

We prove uniqueness of solutions to the Cauchy problem for the derivative nonlinear Schr\"odinger equation in $L^\infty_tH^{1/2}_x$. Our proof is based on the method of normal form reduction (NFR), which has been employed to obtain the…

Analysis of PDEs · Mathematics 2025-12-23 Nobu Kishimoto

We establish existence and uniqueness of solutions to evolutive fractional Mean Field Game systems with regularizing coupling, for any order of the fractional Laplacian $s\in(0,1)$. The existence is addressed via the vanishing viscosity…

Analysis of PDEs · Mathematics 2019-01-09 Marco Cirant , Alessandro Goffi

Time-fractional parabolic equations with a Caputo time derivative of order $\alpha\in(0,1)$ are discretized in time using continuous collocation methods. For such discretizations, we give sufficient conditions for existence and uniqueness…

Numerical Analysis · Mathematics 2024-07-01 Sebastian Franz , Natalia Kopteva