scholarly journals Some Existence and Stability Criteria to a Generalized FBVP Having Fractional Composite p -Laplacian Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Sh. Rezapour ◽  
S. T. M. Thabet ◽  
M. M. Matar ◽  
J. Alzabut ◽  
S. Etemad
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Degree Theory ◽  
Laplacian Operator ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we consider a generalized Caputo boundary value problem of fractional differential equation with composite p -Laplacian operator. Boundary value conditions of this problem are of three-point integral type. First, we obtain Green’s function in relation to the proposed fractional boundary value problem and then for establishing the existence and uniqueness results, we use topological degree theory and Banach contraction principle. Further, we consider a stability analysis of Ulam-Hyers and Ulam-Hyers-Rassias type. To examine the validity of theoretical results, we provide an illustrative example.

scholarly journals On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Hüseyin Aktuğlu ◽  
Mehmet Ali Özarslan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Laplacian Operator ◽  
Fractional Boundary Value Problem ◽  
Solvability Conditions ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

We consider the model of a Caputo -fractional boundary value problem involving -Laplacian operator. By using the Banach contraction mapping principle, we prove that, under some conditions, the suggested model of the Caputo -fractional boundary value problem involving -Laplacian operator has a unique solution for both cases of and . It is interesting that in both cases solvability conditions obtained here depend on , , and the order of the Caputo -fractional differential equation. Finally, we illustrate our results with some examples.

scholarly journals Solvability for Discrete Fractional Boundary Value Problems with ap-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Weidong Lv
Keyword(s):  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Laplacian Operator ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Fractional Boundary Value Problems ◽  
Banach Contraction Mapping

This paper is concerned with the solvability for a discrete fractionalp-Laplacian boundary value problem. Some existence and uniqueness results are obtained by means of the Banach contraction mapping principle. Additionally, two representative examples are presented to illustrate the effectiveness of the main results.

scholarly journals Existence and uniqueness results for a class of fractional differential equations with an integral fractional boundary condition

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1241-1249 ◽  
Author(s):  
Asghar Ahmadkhanlu
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Order Differential Equation ◽  
Necessary Conditions ◽  
Boundary Value ◽  
Fractional Order Differential Equation ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Sufficient And Necessary Conditions ◽  
Fractional Differential

The aim of this work is to study a class of boundary value problem including a fractional order differential equation. Sufficient and necessary conditions will be presented for the existence and uniqueness of solution of this fractional boundary value problem.

scholarly journals Stability Results for a Coupled System of Impulsive Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 927 ◽  
Author(s):  
Akbar Zada ◽  
Shaheen Fatima ◽  
Zeeshan Ali ◽  
Jiafa Xu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Coupled System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Stability Results ◽  
Theoretical Results

In this paper, we establish sufficient conditions for the existence, uniqueness and Ulam–Hyers stability of the solutions of a coupled system of nonlinear fractional impulsive differential equations. The existence and uniqueness results are carried out via Banach contraction principle and Schauder’s fixed point theorem. The main theoretical results are well illustrated with the help of an example.

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 New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative

2019 ◽  
Vol 27 (2) ◽  
pp. 113-141
Author(s):  
Yacine Arioua ◽  
Maria Titraoui
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Nonlinear Fractional Differential Equations ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Fractional Differential

AbstractIn this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel’skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main 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 A boundary value problem for second-order nonlinear difference equations on the integers

2005 ◽  
Vol 47 (2) ◽  
pp. 237-248
Author(s):  
F. Dal ◽  
G. Sh. Guseinov
Keyword(s):  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Second Order ◽  
Nonlinear Difference Equations ◽  
Left Hand ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Limit Circle Case ◽  
Difference Expression

AbstractIn this study, we are concerned with a boundary value problem (BVP) for nonlinear difference equations on the set of all integers Z. under the assumption that the left-hand side is a second-order linear difference expression which belongs to the so-called Weyl-Hamburger limit-circle case. The BVP is considered in the Hilbert space l2 and includes boundary conditions at infinity. Existence and uniqueness results for solution of the considered BVP are established.

scholarly journals On Caputo–Riemann–Liouville Type Fractional Integro-Differential Equations with Multi-Point Sub-Strip Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1899
Author(s):  
Ahmed Alsaedi ◽  
Amjad F. Albideewi ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Liouville Type ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

In this paper, we derive existence and uniqueness results for a nonlinear Caputo–Riemann–Liouville type fractional integro-differential boundary value problem with multi-point sub-strip boundary conditions, via Banach and Krasnosel’skii⏝’s fixed point theorems. Examples are included for the illustration of the obtained results.

scholarly journals Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value Problems

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 671 ◽  
Author(s):  
Surang Sitho ◽  
Chayapat Sudprasert ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Integral Boundary ◽  
Fractional Quantum ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Alternative ◽  
Banach Contraction

In this paper, we study the existence and uniqueness results for noninstantaneous impulsive fractional quantum Hahn integro-difference boundary value problems with integral boundary conditions, by using Banach contraction mapping principle and Leray–Schauder nonlinear alternative. Examples are included illustrating the obtained results. To the best of our knowledge, no work has reported on the existence of solutions to the Hahn-difference equation with noninstantaneous impulses.

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