Existence and Uniqueness for a System of Caputo-Hadamard Fractional Differential Equations with Multipoint Boundary Conditions

In this paper, we study existence and uniqueness of solutions for a system of Caputo-Hadamard fractional differential equations supplemented with multi-point boundary conditions. Our results are based on some classical fixed point theorems such as Banach contraction mapping principle, Leray-Schauder fixed point theorems. At last, we have presented two examples for the illustration of main results.

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Positive solutions for generalized two-term fractional differential equations with integral boundary conditions

Journal of Mathematical Analysis and Modeling ◽

10.48185/jmam.v1i1.35 ◽

2020 ◽

Vol 1 (1) ◽

pp. 47-63

Author(s):

Hanan A. Wahash ◽

Satish K. Panchal

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Upper And Lower Solutions ◽

Integral Boundary Conditions ◽

Integral Boundary ◽

Fractional Differential

In this paper, we consider a class of boundary value problems for nonlinear two-term fractional differential equations with integral boundary conditions involving two $\psi $-Caputo fractional derivative. With the help of the properties Green function, the fixed point theorems of Schauder and Banach, and the method of upper and lower solutions, we derive the existence and uniqueness of positive solution of a proposed problem. Finally, an example is provided to illustrate the acquired results.

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Separated Boundary Value Problems of Sequential Caputo and Hadamard Fractional Differential Equations

Journal of Function Spaces ◽

10.1155/2018/6974046 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 6

Author(s):

Jessada Tariboon ◽

Asawathep Cuntavepanit ◽

Sotiris K. Ntouyas ◽

Woraphak Nithiarayaphaks

Keyword(s):

Differential Equations ◽

Boundary Value Problems ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Boundary Value ◽

Uniqueness Of Solutions ◽

Hadamard Fractional Differential Equations ◽

Fractional Differential ◽

Sequential Fractional Differential Equations

In this paper, we discuss the existence and uniqueness of solutions for new classes of separated boundary value problems of Caputo-Hadamard and Hadamard-Caputo sequential fractional differential equations by using standard fixed point theorems. We demonstrate the application of the obtained results with the aid of examples.

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Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations

Proyecciones (Antofagasta) ◽

10.22199/issn.0717-6279-2021-01-0009 ◽

2021 ◽

Vol 40 (1) ◽

pp. 139-152

Author(s):

Abdelouaheb Ardjouni

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Positive Solution ◽

Positive Solutions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Upper And Lower Solutions ◽

Hadamard Fractional Differential Equations ◽

Fractional Differential

We prove the existence and uniqueness of a positive solution of nonlinear Caputo-Hadamard fractional differential equations. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.

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Existence and Uniqueness of Solutions for the Nonlinear Fractional Differential Equations with Two-point and Integral Boundary Conditions

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v14i2.3978 ◽

2021 ◽

Vol 14 (2) ◽

pp. 608-617

Author(s):

Yagub Sharifov ◽

S.A. Zamanova ◽

R.A. Sardarova

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Integral Boundary Conditions ◽

Contraction Mapping Principle ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

Fractional Differential

In this paper the existence and uniqueness of solutions to the fractional differential equations with two-point and integral boundary conditions is investigated. The Green function is constructed, and the problem under consideration is reduced to the equivalent integral equation. Existence and uniqueness of a solution to this problem is analyzed using the Banach the contraction mapping principle and Krasnoselskii’s fixed point theorem.

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Coupled Systems of Sequential Caputo and Hadamard Fractional Differential Equations with Coupled Separated Boundary Conditions

Symmetry ◽

10.3390/sym10120701 ◽

2018 ◽

Vol 10 (12) ◽

pp. 701 ◽

Cited By ~ 7

Author(s):

Suphawat Asawasamrit ◽

Sotiris Ntouyas ◽

Jessada Tariboon ◽

Woraphak Nithiarayaphaks

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Coupled Systems ◽

Uniqueness Of Solutions ◽

Krasnoselskii’S Fixed Point Theorem ◽

Hadamard Fractional Differential Equations ◽

Special Cases ◽

Separated Boundary Conditions ◽

Fractional Differential

This paper studies the existence and uniqueness of solutions for a new coupled system of nonlinear sequential Caputo and Hadamard fractional differential equations with coupled separated boundary conditions, which include as special cases the well-known symmetric boundary conditions. Banach’s contraction principle, Leray–Schauder’s alternative, and Krasnoselskii’s fixed-point theorem were used to derive the desired results, which are well-illustrated with examples.

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Existence and uniqueness of solutions for nonlinear implicit Caputo-Hadamard fractional differential equations with nonlocal conditions

Advances in the Theory of Nonlinear Analysis and its Application ◽

10.31197/atnaa.501118 ◽

2019 ◽

Vol 3 (1) ◽

pp. 46-52 ◽

Cited By ~ 1

Author(s):

Abdelouaheb Ardjouni ◽

Ahcene Djoudi

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Nonlocal Conditions ◽

Uniqueness Of Solutions ◽

Hadamard Fractional Differential Equations ◽

Fractional Differential

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A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions

Abstract and Applied Analysis ◽

10.1155/2012/818703 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 16

Author(s):

Bashir Ahmad ◽

Sotiris K. Ntouyas

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Fixed Point Theorems ◽

Existence And Uniqueness Results ◽

New Class ◽

Uniqueness Results ◽

Separated Boundary Conditions ◽

Fractional Differential

We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.

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Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions

Acta Mathematica Scientia ◽

10.1016/s0252-9602(11)60388-3 ◽

2011 ◽

Vol 31 (6) ◽

pp. 2122-2130 ◽

Cited By ~ 18

Author(s):

Bashir Ahmad ◽

Juan J. Nieto ◽

Ahmed Alsaedi

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Integral Boundary Conditions ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

Nonlinear Fractional Differential Equations ◽

Type Integral ◽

Fractional Differential

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EXISTENCE AND UNIQUENESS RESULTS FOR A COUPLED SYSTEM OF HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT BOUNDARY CONDITIONS

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi2003843h ◽

2020 ◽

pp. 843

Author(s):

Mohamed Houas ◽

Khellaf Ould Melha

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Coupled System ◽

Point Boundary ◽

Uniqueness Of Solutions ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Hadamard Fractional Differential Equations ◽

Fractional Differential

In this paper, we have studied existence and uniqueness of solutions for a coupled system of multi-point boundary value problems for Hadamard fractional differential equations. By applying principle contraction and Shaefer's fixed point theorem new existence results have been obtained.

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A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2019-0034 ◽

2019 ◽

Vol 22 (3) ◽

pp. 601-618 ◽

Cited By ~ 12

Author(s):

Bashir Ahmad ◽

Najla Alghamdi ◽

Ahmed Alsaedi ◽

Sotiris K. Ntouya

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Significant Contribution ◽

Uniqueness Of Solutions ◽

Coupled Boundary Conditions ◽

Fractional Differential ◽

Banach’S Contraction Principle

Abstract This paper studies the existence and uniqueness of solutions for a new boundary value problem of coupled nonlinear multi-term fractional differential equations supplemented with three-point coupled boundary conditions. We make use of Banach’s contraction principle and Leray-Schauder’s alternative to derive the desired results, which are well illustrated with examples. We emphasize that the obtained results are new and make a significant contribution to the existing literature on the topic.

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