Existence theory for fractional differential equations with nonlocal integro-multipoint boundary conditions with applications

2019 ◽  
pp. 271-282
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Existence Theory ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

scholarly journals Generalized Liouville–Caputo Fractional Differential Equations and Inclusions with Nonlocal Generalized Fractional Integral and Multipoint Boundary Conditions

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 667 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Madeaha Alghanmi ◽  
Bashir Ahmad ◽  
Sotiris Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fractional Integral ◽  
Integral Boundary ◽  
Multipoint Boundary ◽  
Generalized Fractional Integral ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Differential Equations And Inclusions

We develop the existence criteria for solutions of Liouville–Caputo-type generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral and multipoint boundary conditions. Modern techniques of functional analysis are employed to derive the main results. Examples illustrating the main results are also presented. It is imperative to mention that our results correspond to the ones for a symmetric second-order nonlocal multipoint integral boundary value problem under suitable conditions (see the last section).

scholarly journals On a coupled system of higher order nonlinear Caputo fractional differential equations with coupled Riemann–Stieltjes type integro-multipoint boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Ymnah Alruwaily ◽  
Sotiris K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Multipoint Boundary ◽  
Uniqueness Results ◽  
Caputo Fractional Differential Equations ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Stieltjes Type

AbstractWe study a coupled system of Caputo fractional differential equations with coupled non-conjugate Riemann–Stieltjes type integro-multipoint boundary conditions. Existence and uniqueness results for the given boundary value problem are obtained by applying the Leray–Schauder nonlinear alternative, the Krasnoselskii fixed point theorem and Banach’s contraction mapping principle. Examples are constructed to illustrate the obtained results.

Positive solutions for a system of nonlocal fractional boundary value problems

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Johnny Henderson ◽  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Hammerstein Integral Equations ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

AbstractWe investigate the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to multipoint boundary conditions. Existence results for systems of nonlinear Hammerstein integral equations are also presented. Some nontrivial examples are included.

scholarly journals A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Existence Theory ◽  
Liouville Type ◽  
Arbitrary Length ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential

We develop the existence theory for nonlinear fractional differential equations of arbitrary order with Riemann-Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Our results are based on some standard tools of fixed point theory. For the illustration of the results, some examples are also discussed.

A Study of Coupled Systems of ψ-Hilfer Type Sequential Fractional Differential Equations with Integro-Multipoint Boundary Conditions

2021 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Ayub Samadi ◽  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Coupled Systems ◽  
Uniqueness Of Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

In this paper, the existence and uniqueness of solutions for a coupled system of ψ-Hilfer type sequential fractional differential equations supplemented with nonlocal integro-multi-point boundary conditions is investigated. The presented results are obtained via the classical Banach and Krasnosel’skiĭ’s fixed point theorems and the Leray–Schauder alternative. Examples are included to illustrate the effectiveness of the obtained results.

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