Hilfer-Hadamard Nonlocal Integro-Multipoint Fractional Boundary Value Problems

This paper is concerned with the existence and uniqueness of solutions for a new class of boundary value problems, consisting by Hilfer-Hadamard fractional differential equations, supplemented with nonlocal integro-multipoint boundary conditions. The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying Schaefer and Krasnoselskii fixed point theorems as well as Leray-Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

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Some Properties of Solutions to Multiterm Fractional Boundary Value Problems with p -Laplacian Operator

Journal of Function Spaces ◽

10.1155/2021/7527306 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

KumSong Jong ◽

HuiChol Choi ◽

KyongJun Jang ◽

SongGuk Jong ◽

KyongSon Jon ◽

...

Keyword(s):

Boundary Value Problems ◽

Boundary Value ◽

Contraction Mapping Principle ◽

Laplacian Operator ◽

Banach Contraction ◽

Fractional Differential ◽

Multipoint Boundary Value Problems ◽

The Given ◽

Banach Contraction Mapping Principle ◽

Banach Contraction Mapping

In this paper, we study some properties of positive solutions to a class of multipoint boundary value problems for nonlinear multiterm fractional differential equations with p -Laplacian operator. Using the Banach contraction mapping principle, the existence, the uniqueness, the positivity, and the continuous dependency on m -point boundary conditions of the solutions to the given problem are investigated. Also, two examples are presented to demonstrate our main results.

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Sequential Riemann–Liouville and Hadamard–Caputo Fractional Differential Systems with Nonlocal Coupled Fractional Integral Boundary Conditions

Axioms ◽

10.3390/axioms10030174 ◽

2021 ◽

Vol 10 (3) ◽

pp. 174

Author(s):

Chanakarn Kiataramkul ◽

Weera Yukunthorn ◽

Sotiris K. Ntouyas ◽

Jessada Tariboon

Keyword(s):

Boundary Conditions ◽

Fractional Integral ◽

Integral Boundary Conditions ◽

Contraction Mapping Principle ◽

Uniqueness Of Solutions ◽

Caputo Fractional Derivatives ◽

Integral Boundary ◽

Banach Contraction ◽

Fractional Differential ◽

Banach Contraction Mapping Principle

In this paper, we initiate the study of existence of solutions for a fractional differential system which contains mixed Riemann–Liouville and Hadamard–Caputo fractional derivatives, complemented with nonlocal coupled fractional integral boundary conditions. We derive necessary conditions for the existence and uniqueness of solutions of the considered system, by using standard fixed point theorems, such as Banach contraction mapping principle and Leray–Schauder alternative. Numerical examples illustrating the obtained results are also presented.

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Existence and uniqueness of solutions for a mixed p-Laplace boundary value problem involving fractional derivatives

Advances in Difference Equations ◽

10.1186/s13662-020-03154-2 ◽

2020 ◽

Vol 2020 (1) ◽

Author(s):

Shuqi Wang ◽

Zhanbing Bai

Keyword(s):

Boundary Value Problem ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Boundary Value ◽

Contraction Mapping Principle ◽

Uniqueness Of Solutions ◽

Novel Approach ◽

Banach Contraction ◽

Left And Right ◽

Banach Contraction Mapping Principle

AbstractIn this article, the existence and uniqueness of solutions for a multi-point fractional boundary value problem involving two different left and right fractional derivatives with p-Laplace operator is studied. A novel approach is used to acquire the desired results, and the core of the method is Banach contraction mapping principle. Finally, an example is given to verify the results.

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Noninstantaneous Impulsive Fractional Quantum Hahn Integro-Difference Boundary Value Problems

Mathematics ◽

10.3390/math8050671 ◽

2020 ◽

Vol 8 (5) ◽

pp. 671 ◽

Cited By ~ 2

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

Abstract and Applied Analysis ◽

10.1155/2013/658617 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 5

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.

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Multi-Point and Anti-Periodic Conditions for Generalized Langevin Equation with Two Fractional Orders

Fractal and Fractional ◽

10.3390/fractalfract3040051 ◽

2019 ◽

Vol 3 (4) ◽

pp. 51 ◽

Cited By ~ 8

Author(s):

Ahmed Salem ◽

Balqees Alghamdi

Keyword(s):

Langevin Equation ◽

Contraction Mapping Principle ◽

Generalized Langevin Equation ◽

Uniqueness Of Solutions ◽

Caputo Fractional Derivatives ◽

New Class ◽

Banach Contraction ◽

Derivatives Of ◽

Fractional Orders ◽

Banach Contraction Mapping Principle

With anti-periodic and a new class of multi-point boundary conditions, we investigate, in this paper, the existence and uniqueness of solutions for the Langevin equation that has Caputo fractional derivatives of two different orders. Existence of solutions is obtained by applying Krasnoselskii–Zabreiko’s and the Leray–Schauder fixed point theorems. The Banach contraction mapping principle is used to investigate the uniqueness. Illustrative examples are provided to apply of the fundamental investigations.

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Hilfer–Hadamard Fractional Boundary Value Problems with Nonlocal Mixed Boundary Conditions

Fractal and Fractional ◽

10.3390/fractalfract5040195 ◽

2021 ◽

Vol 5 (4) ◽

pp. 195

Author(s):

Bashir Ahmad ◽

Sotiris K. Ntouyas

Keyword(s):

Boundary Conditions ◽

Mixed Boundary ◽

Mixed Boundary Conditions ◽

Contraction Mapping Principle ◽

Existence Results ◽

Uniqueness Of Solutions ◽

Banach Contraction ◽

Fractional Differential ◽

Banach Contraction Mapping Principle ◽

Banach Contraction Mapping

This paper is concerned with the existence and uniqueness of solutions for a Hilfer–Hadamard fractional differential equation, supplemented with mixed nonlocal (multi-point, fractional integral multi-order and fractional derivative multi-order) boundary conditions. The existence of a unique solution is obtained via Banach contraction mapping principle, while the existence results are established by applying the fixed point theorems due to Krasnoselskiĭ and Schaefer and Leray–Schauder nonlinear alternatives. We demonstrate the application of the main results by presenting numerical examples. We also derive the existence results for the cases of convex and non-convex multifunctions involved in the multi-valued analogue of the problem at hand.

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Nonlocal Fractional Boundary Value Problems with Slit-Strips Boundary Conditions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2015-0017 ◽

2015 ◽

Vol 18 (1) ◽

Cited By ~ 17

Author(s):

Bashir Ahmad ◽

Sotiris K. Ntouyas

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Boundary Value ◽

Nonlocal Boundary ◽

Integral Boundary Conditions ◽

Contraction Mapping Principle ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

Nonlinear Alternative ◽

Differential Equations And Inclusions

AbstractIn this paper, we study nonlocal boundary value problems of fractional differential equations and inclusions with slit-strips integral boundary conditions. We show the existence and uniqueness of solutions for the single valued case (equations) by means of classical contraction mapping principle while the existence result is obtained via a fixed point theorem due to D. O'Regan. The existence of solutions for the multivalued case (inclusions) is established via nonlinear alternative for contractive maps. The results are well illustrated with the aid of examples.

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Existence of solutions of boundary value problems for nonlinear fractional differential equations with integral conditions

Proyecciones (Antofagasta) ◽

10.22199/issn.0717-6279-4271 ◽

2021 ◽

Vol 40 (5) ◽

pp. 1117-1135

Author(s):

Ahcene Boukehila

Keyword(s):

Differential Equations ◽

Fractional Derivative ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Nonlinear Term ◽

Boundary Value ◽

Integral Conditions ◽

Uniqueness Of Solutions ◽

Banach Contraction ◽

Fractional Differential

In this work we investigate the existence and uniqueness of solutions of boundary value problems for fractional differential equations involving the Caputo fractional derivative with integral conditions and the nonlinear term depends on the fractional derivative of an unknown function. Our existence results are based on Banach contraction principle and Schauder fixed point theorem. Two examples are provided to illustrate our results.

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Impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function

Advances in Difference Equations ◽

10.1186/s13662-019-2416-6 ◽

2019 ◽

Vol 2019 (1) ◽

Cited By ~ 2

Author(s):

Chanon Promsakon ◽

Eakachai Suntonsinsoungvon ◽

Sotiris K. Ntouyas ◽

Jessada Tariboon

Keyword(s):

Fractional Derivative ◽

Boundary Value Problems ◽

Caputo Fractional Derivative ◽

Boundary Value ◽

Contraction Mapping Principle ◽

Uniqueness Result ◽

New Class ◽

Nonlinear Alternative ◽

Separated Boundary Conditions ◽

Fractional Boundary Value Problems

AbstractIn this paper, we study the existence and uniqueness for a new class of impulsive fractional boundary value problems with separated boundary conditions containing the Caputo fractional derivative of a function with respect to another function. The existence of solutions is established by using the Leray–Schauder nonlinear alternative, and the uniqueness result is proved via Banach’s contraction mapping principle. Some examples are also constructed to demonstrate the application of main results.

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