scholarly journals Nonlocal coupled hybrid fractional system of mixed fractional derivatives via an extension of Darbo's theorem

2021 ◽  
Vol 6 (4) ◽  
pp. 3915-3926
Author(s):  
Ayub Samadi ◽  
◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon ◽  
◽  
...  
Keyword(s):  
Fractional Derivatives ◽  
Fractional System ◽  
Mixed Fractional Derivatives

scholarly journals On the General Solution of Impulsive Systems with Hadamard Fractional Derivatives

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Xianmin Zhang ◽  
Xianzhen Zhang ◽  
Zuohua Liu ◽  
Wenbin Ding ◽  
Hui Cao ◽  
...  
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Theoretical Result ◽  
Fractional Derivatives ◽  
Impulsive Differential Equations ◽  
Limit Case ◽  
Impulsive Systems ◽  
Fractional System ◽  
Approach Zero

This paper is concerned with the solution for impulsive differential equations with Hadamard fractional derivatives. The general solution of this impulsive fractional system is found by considering the limit case in which impulses approach zero. Next, an example is provided to expound the theoretical result.

scholarly journals Nonlocal Fractional Hybrid Boundary Value Problems Involving Mixed Fractional Derivatives and Integrals via a Generalization of Darbo’s Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ayub Samadi ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problem ◽  
Theoretical Result ◽  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Boundary Value ◽  
Measures Of Noncompactness ◽  
Fractional Derivatives And Integrals ◽  
Mixed Fractional Derivatives

In this work, a new existence result is established for a nonlocal hybrid boundary value problem which contains one left Caputo and one right Riemann–Liouville fractional derivatives and integrals. The main result is proved by applying a new generalization of Darbo’s theorem associated with measures of noncompactness. Finally, an example to justify the theoretical result is also presented.

scholarly journals Instantaneous blow-up of solutions to the Cauchy problem for the fractional Khokhlov-Zabolotskaya equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1266-1271
Author(s):  
Mohamed Jleli
Keyword(s):  
Cauchy Problem ◽  
Nonlinear Equation ◽  
Fractional Derivatives ◽  
Blow Up ◽  
Second Order ◽  
Nonlinear Capacity ◽  
The Cauchy Problem ◽  
Mixed Fractional Derivatives ◽  
Order Nonlinear Equation ◽  
Capacity Method

Abstract In this paper, we consider the Cauchy problem for a second-order nonlinear equation with mixed fractional derivatives related to the fractional Khokhlov-Zabolotskaya equation. We prove the nonexistence of a classical local in time solution. The obtained instantaneous blow-up result is proved via the nonlinear capacity method.

scholarly journals On the Parametrization of Nonlinear Impulsive Fractional Integro–Differential System With Non-Separated Integral Coupled Boundary Conditions

2020 ◽  
Vol 8 (4) ◽  
pp. 160-168
Author(s):  
Ava Sh. Rafeeq
Keyword(s):  
Boundary Conditions ◽  
Periodic Solutions ◽  
Differential System ◽  
Fractional Derivatives ◽  
Main Idea ◽  
Coupled Boundary Conditions ◽  
Fractional System ◽  
Sequence Of Functions

We give a new investigation of periodic solutions of nonlinear impulsive fractional integro-differential system with different orders of fractional derivatives with non-separated integral coupled boundary conditions. Uniformly Converging of the sequence of functions according to the main idea of the Numerical-analytic technique, from creating a sequence of functions. An example of impulsive fractional system is also presented to illustrate the theory.

scholarly journals Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 117 ◽  
Author(s):  
Suphawat Asawasamrit ◽  
Woraphak Nithiarayaphaks ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Nonlocal Conditions ◽  
Ulam Stability ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Mixed Fractional Derivatives

In this paper, we study the existence and uniqueness of solution for fractional differential equations with mixed fractional derivatives, integrals and multi-point conditions. After that, we also establish different kinds of Ulam stability for the problem at hand. Examples illustrating our results are also presented.

A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations

2016 ◽  
Vol 19 (3) ◽  
pp. 733-757 ◽  
Author(s):  
Boling Guo ◽  
Qiang Xu ◽  
Ailing Zhu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Fractional Derivatives ◽  
Second Order ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Mixed Fractional Derivatives ◽  
The Fourier Transform ◽  
Nicolson Scheme

AbstractA finite difference method which is second-order accurate in time and in space is proposed for two-dimensional fractional percolation equations. Using the Fourier transform, a general approximation for the mixed fractional derivatives is analyzed. An approach based on the classical Crank-Nicolson scheme combined with the Richardson extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Consistency, stability and convergence of the method are established. Numerical experiments illustrating the effectiveness of the theoretical analysis are provided.

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