scholarly journals Nonlocal Boundary Value Problems forq-Difference Equations and Inclusions

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Quantum Numbers

We study boundary value problems forq-difference equations and inclusions with nonlocal and integral boundary conditions which have different quantum numbers. Some new existence and uniqueness results are obtained by using fixed point theorems. Examples are given to illustrate the results.

scholarly journals Nonlocal boundary value problems for ψ-Hilfer fractional-order Langevin equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Cholticha Nuchpong ◽  
Sotiris K. Ntouyas ◽  
Devaraj Vivek ◽  
Jessada Tariboon
Keyword(s):  
Fractional Order ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Langevin Equations ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

AbstractIn the paper, we study a boundary value problem for a class of ψ-Hilfer fractional-order Langevin equations with multi-point integral boundary conditions. Existence and uniqueness results are established by using well-known fixed point theorems. Examples illustrating the main results are also included.

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.

scholarly journals A STUDY OF NONLINEAR FRACTIONAL-ORDER BOUNDARY VALUE PROBLEM WITH NONLOCAL ERDELYI-KOBER AND GENERALIZED RIEMANN-LIOUVILLE TYPE INTEGRAL BOUNDARY CONDITIONS

2017 ◽  
Vol 22 (2) ◽  
pp. 121-139 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Conditions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Fractional Integrals ◽  
Integral Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Caputo Fractional Differential Equations ◽  
The Given

We investigate a new kind of nonlocal boundary value problems of nonlinear Caputo fractional differential equations supplemented with integral boundary conditions involving Erdelyi-Kober and generalized Riemann-Liouville fractional integrals. Existence and uniqueness results for the given problem are obtained by means of standard fixed point theorems. Examples illustrating the main results are also discussed.

scholarly journals Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 130
Author(s):  
Suphawat Asawasamrit ◽  
Yasintorn Thadang ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Nonlinear Alternative

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

scholarly journals On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hussein A. H. Salem ◽  
Mieczysław Cichoń
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Point Of View ◽  
Integral Boundary ◽  
Special Cases

The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.

scholarly journals Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1905
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

scholarly journals Notes on Local and Nonlocal Intuitionistic Fuzzy Fractional Boundary Value Problems with Caputo Fractional Derivatives

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Ali El Mfadel ◽  
Said Melliani ◽  
M’hamed Elomari
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Caputo Fractional Derivatives ◽  
Existence And Uniqueness Results ◽  
Intuitionistic Fuzzy ◽  
Uniqueness Results ◽  
Fractional Boundary Value Problems

In this paper, we investigate the existence and uniqueness results of intuitionistic fuzzy local and nonlocal fractional boundary value problems by employing intuitionistic fuzzy fractional calculus and some fixed-point theorems. As an application, we conclude this manuscript by giving an example to illustrate the obtained results.

Solvability for nonlocal boundary value problems with generalized 𝑝-Laplacian on an unbounded domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Marek Matyjasik ◽  
Katarzyna Szymańska-Dȩbowska
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Nonlinear Boundary Value Problems ◽  
Integral Boundary ◽  
Positive Half

Abstract This paper is devoted to the existence of solutions for a class of nonlinear boundary value problems with integral boundary conditions and generalized 𝑝-Laplacian on the positive half-line. We establish sufficient conditions to guarantee the existence of solutions in a special function space by using Leray–Schauder-type arguments. Examples are also given to illustrate the main results.

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