scholarly journals On the existence and stability of solution of boundary value problem for fractional integro-differential equations with complex order

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2901-2910 ◽  
Author(s):  
E.M. Elsayed ◽  
K. Kanagarajan ◽  
D. Vivek
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Stability Of Solutions ◽  
Complex Order ◽  
Stability Of Solution ◽  
Banach Contraction ◽  
Existence And Stability ◽  
The Banach Contraction Principle

In this paper, we establish sufficient conditions for the existence and stability of solutions for fractional integro-differential equations with boundary conditions involving complex order. The proofs are based upon the Banach contraction principle. An example is included to show the applicability of our results.

scholarly journals Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order

2015 ◽  
Vol 1 (1) ◽  
pp. 22-37 ◽  
Author(s):  
Mouffak Benchohra ◽  
Soufyane Bouriah
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Fractional Differential ◽  
The Banach Contraction Principle ◽  
Stability Results ◽  
Implicit Fractional Differential Equations

Abstract In this paper, we establish sufficient conditions for the existence and stability of solutions for a class of boundary value problem for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle. Two examples are included to show the applicability of our results.

scholarly journals On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 476
Author(s):  
Jiraporn Reunsumrit ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
The Banach Contraction Principle

In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.

scholarly journals Triangular System of Higher Order Singular Fractional Differential Equations

2021 ◽  
Vol 45 (01) ◽  
pp. 81-101
Author(s):  
AMELE TAIEB ◽  
ZOUBIR DAHMANI
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
High Dimensional ◽  
Dimensional System ◽  
Stability Of Solutions ◽  
Banach Contraction ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
The Banach Contraction Principle

In this paper, we introduce a high dimensional system of singular fractional differential equations. Using Schauder fixed point theorem, we prove an existence result. We also investigate the uniqueness of solution using the Banach contraction principle. Moreover, we study the Ulam-Hyers stability and the generalized-Ulam-Hyers stability of solutions. Some illustrative examples are also presented.

Existence of nonoscillatory solutions of higher order neutral differential equations with distributed deviating arguments

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
T. Candan ◽  
R. Dahiya
Keyword(s):  
Differential Equations ◽  
Variable Coefficient ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonoscillatory Solutions ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Distributed Deviating Arguments ◽  
Banach Contraction ◽  
The Banach Contraction Principle

AbstractIn this work, we consider the existence of nonoscillatory solutions of variable coefficient higher order linear neutral differential equations with distributed deviating arguments. We use the Banach contraction principle to obtain new sufficient conditions, which are weaker than those known, for the existence of nonoscillatory solutions.

L 1-solutions of the boundary value problem for implicit fractional order differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Abstract The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

scholarly journals Boundary Value Problem for Nonlinear Implicit Generalized Hilfer-Type Fractional Differential Equations with Impulses

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Gaston N’Guérékata
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Banach Contraction ◽  
Fractional Differential ◽  
The Banach Contraction Principle ◽  
Stability Results ◽  
Rassias Stability ◽  
Implicit Fractional Differential Equations

This article deals with some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer Fractional derivative. The results are obtained using the Banach contraction principle and Krasnoselskii’s and Schaefer’s fixed-point theorems.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1205
Author(s):  
Usman Riaz ◽  
Akbar Zada ◽  
Zeeshan Ali ◽  
Ioan-Lucian Popa ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Coupled System ◽  
Initial Boundary ◽  
Liouville Type ◽  
Liouville Derivative ◽  
Banach Contraction ◽  
Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

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