scholarly journals The non-uniqueness of solution for initial value problem of impulsive differential equations involving higher order Katugampola fractional derivative

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xian-Min Zhang
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Impulsive Differential Equations ◽  
Higher Order ◽  
Uniqueness Of Solution ◽  
Initial Value

scholarly journals Nonlocal Initial Value Problem for Hybrid Generalized Hilfer-type Fractional Implicit Differential Equations

2021 ◽  
Vol 8 (1) ◽  
pp. 87-100
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Juan J. Nieto ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Banach Algebras ◽  
Existence Results ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
Implicit Differential Equations

Abstract In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

AN EFFECTIVE CAUCHY-PEANO EXISTENCE THEOREM FOR UNIQUE SOLUTIONS

1996 ◽  
Vol 07 (02) ◽  
pp. 151-160 ◽  
Author(s):  
KEIJO RUOHONEN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Existence Theorem ◽  
Initial Value Problem ◽  
Uniqueness Of Solution ◽  
Time Interval ◽  
Initial Value ◽  
Initial Values ◽  
Systems Of Odes

It is shown in this paper that the solution of the initial value problem for a system of ordinary differential equations is computable if the following assumptions are satisfied: The time interval considered is computable, the system is continuous and computable, the initial values are computable, the system is effectively bounded, and the solution is unique. It should be mentioned that for a single ODE this follows immediately from the standard proof of Osgood’s existence theorem, but this approach is not available for systems of ODEs. The key assumption here is uniqueness of solution: a result of Pour-El’s and Richards’ shows that nonunique solutions may be noncomputable, even for a single ODE.

scholarly journals The System of Differential Equations Associated With Involutions

2021 ◽  
Author(s):  
Farrukh Nuriddin ugli Dekhkonov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Initial Value Problem ◽  
Initial Conditions ◽  
Higher Order ◽  
System Of Differential Equations ◽  
Initial Value ◽  
Order Ordinary Differential Equation

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

scholarly journals Study of implicit-impulsive differential equations involving Caputo-Fabrizio fractional derivative

2021 ◽  
Vol 7 (3) ◽  
pp. 4017-4037
Author(s):  
Thanin Sitthiwirattham ◽  
◽  
Rozi Gul ◽  
Kamal Shah ◽  
Ibrahim Mahariq ◽  
...  
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equations ◽  
Initial Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Impulsive Fractional Differential Equations ◽  
Non Local ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

<abstract><p>This article is devoted to investigate a class of non-local initial value problem of implicit-impulsive fractional differential equations (IFDEs) with the participation of the Caputo-Fabrizio fractional derivative (CFFD). By means of Krasnoselskii's fixed-point theorem and Banach's contraction principle, the results of existence and uniqueness are obtained. Furthermore, we establish some results of Hyers-Ulam (H-U) and generalized Hyers-Ulam (g-H-U) stability. Finally, an example is provided to demonstrate our results.</p></abstract>

scholarly journals On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

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