Existence Theory forq-Antiperiodic Boundary Value Problems of Sequentialq-Fractional Integrodifferential Equations

We discuss the existence and uniqueness of solutions for a new class of sequentialq-fractional integrodifferential equations withq-antiperiodic boundary conditions. Our results rely on the standard tools of fixed-point theory such as Krasnoselskii's fixed-point theorem, Leray-Schauder nonlinear alternative, and Banach's contraction principle. An illustrative example is also presented.

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Terminal Value Problem for Differential Equations with Hilfer–Katugampola Fractional Derivative

Symmetry ◽

10.3390/sym11050672 ◽

2019 ◽

Vol 11 (5) ◽

pp. 672 ◽

Cited By ~ 2

Author(s):

Mouffak Benchohra ◽

Soufyane Bouriah ◽

Juan J. Nieto

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Fractional Derivative ◽

Fixed Point Theory ◽

Point Theory ◽

Uniqueness Of Solutions ◽

Krasnoselskii’S Fixed Point Theorem ◽

Banach Contraction ◽

Fractional Differential ◽

Terminal Value Problem

We present in this work the existence results and uniqueness of solutions for a class of boundary value problems of terminal type for fractional differential equations with the Hilfer–Katugampola fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Banach contraction principle and Krasnoselskii’s fixed point theorem. We illustrate our main findings, with a particular case example included to show the applicability of our outcomes.

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RIEMANN–LIOUVILLE FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTIONAL NONLOCAL MULTI-POINT BOUNDARY CONDITIONS

Fractals ◽

10.1142/s0218348x22400023 ◽

2021 ◽

pp. 2240002

Author(s):

BASHIR AHMAD ◽

BADRAH ALGHAMDI ◽

RAVI P. AGARWAL ◽

AHMED ALSAEDI

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Conditions ◽

Existence And Uniqueness ◽

Weighted Space ◽

Fixed Point Theory ◽

Point Theory ◽

Fractional Integrals ◽

Existence Theory ◽

Uniqueness Of Solutions

In this paper, we investigate the existence and uniqueness of solutions for Riemann–Liouville fractional integro-differential equations equipped with fractional nonlocal multi-point and strip boundary conditions in the weighted space. The methods of our study include the well-known tools of the fixed point theory, which are commonly applied to establish the existence theory for the initial and boundary value problems after converting them into the fixed point problems. We also discuss the case when the nonlinearity depends on the Riemann–Liouville fractional integrals of the unknown function. Numerical examples illustrating the main results are presented.

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On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations

Journal of Function Spaces ◽

10.1155/2020/8891736 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Lahcen Ibnelazyz ◽

Karim Guida ◽

Said Melliani ◽

Khalid Hilal

Keyword(s):

Fixed Point ◽

Boundary Value Problem ◽

Fixed Point Theory ◽

Boundary Value ◽

Point Theory ◽

Integrodifferential Equations ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

Integral Boundary Value Problem ◽

Uniqueness Results

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.

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New Existence Results for Nonlinear Fractional Integrodifferential Equations

Advances in Mathematical Physics ◽

10.1155/2021/5525591 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Lahcen Ibnelazyz ◽

Karim Guida ◽

Khalid Hilal ◽

Said Melliani

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Point Theory ◽

Contraction Mapping Principle ◽

Integrodifferential Equations ◽

Krasnoselskii’S Fixed Point Theorem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Banach Contraction ◽

Banach Contraction Mapping Principle

This paper discusses a boundary value problem of nonlinear fractional integrodifferential equations of order 1 < α ≤ 2 and 1 < β ≤ 2 and boundary conditions of the form x 0 = x 1 = D c β x 1 = D c β x 0 = 0 . Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. Moreover, two illustrative examples are studied to support the results.

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Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions

Advances in Mathematical Physics ◽

10.1155/2020/8898292 ◽

2020 ◽

Vol 2020 ◽

pp. 1-8

Author(s):

Karim Guida ◽

Khalid Hilal ◽

Lahcen Ibnelazyz

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Integral Boundary Conditions ◽

Coupled Systems ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

Krasnoselskii’S Fixed Point Theorem ◽

New Class ◽

Nonlocal Integral Boundary Conditions ◽

Banach’S Contraction Principle

This paper deals with the existence and uniqueness of solutions for a new class of coupled systems of Hilfer fractional pantograph differential equations with nonlocal integral boundary conditions. First of all, we are going to give some definitions that are necessary for the understanding of the manuscript; second of all, we are going to prove our main results using the fixed point theorems, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem; in the end, we are giving two examples to illustrate our results.

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Existence results for nonlinear fractional q-difference equations with nonlocal Riemann-Liouville q-integral boundary conditions

Filomat ◽

10.2298/fil1609521y ◽

2016 ◽

Vol 30 (9) ◽

pp. 2521-2533 ◽

Cited By ~ 3

Author(s):

Wengui Yang

Keyword(s):

Fixed Point ◽

Boundary Conditions ◽

Difference Equations ◽

Fixed Point Theory ◽

Integral Boundary Conditions ◽

Point Theory ◽

Uniqueness Of Solutions ◽

Integral Boundary ◽

Nonlinear Alternative ◽

Krasnoselskii Fixed Point Theorem

This paper deals with the existence and uniqueness of solutions for a class of nonlinear fractional q-difference equations boundary value problems involving four-point nonlocal Riemann-Liouville q-integral boundary conditions of different order. Our results are based on some well-known tools of fixed point theory such as Banach contraction principle, Krasnoselskii fixed point theorem, and the Leray-Schauder nonlinear alternative. As applications, some interesting examples are presented to illustrate the main results.

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Fixed point results for mappings satisfying (ψ φ)-weakly contractive condition in ordered partial metric spaces

Mathematica Slovaca ◽

10.2478/s12175-013-0141-2 ◽

2013 ◽

Vol 63 (4) ◽

Cited By ~ 1

Author(s):

Hemant Nashine

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Fixed Point Theory ◽

Point Theory ◽

Contractive Condition ◽

Partial Metric ◽

New Class ◽

Weakly Contractive Condition ◽

Partial Metric Spaces ◽

Weakly Contractive

AbstractIn [18], Matthews introduced a new class of metric spaces, that is, the concept of partial metric spaces, or equivalently, weightable quasi-metrics, are investigated to generalize metric spaces (X, d), to develop and to introduce a new fixed point theory. In partial metric spaces, the self-distance for any point need not be equal to zero. In this paper, we study some results for single map satisfying (ψ,φ)-weakly contractive condition in partial metric spaces endowed with partial order. An example is given to support the useability of our results.

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Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953391000035 ◽

1991 ◽

Vol 4 (1) ◽

pp. 47-69 ◽

Cited By ~ 2

Author(s):

Dajun Guo

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Fixed Point Theory ◽

Index Theory ◽

Point Theory ◽

Second Order ◽

Integrodifferential Equations ◽

Third Order ◽

Nonnegative Solutions ◽

Fixed Point Index Theory

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

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Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Axioms ◽

10.3390/axioms9020059 ◽

2020 ◽

Vol 9 (2) ◽

pp. 59

Author(s):

Ahmed Salem ◽

Mohammad Alnegga

Keyword(s):

Fixed Point ◽

Measure Of Noncompactness ◽

Fixed Point Theory ◽

Point Theory ◽

Existence Of A Solution ◽

New Class ◽

Research Article ◽

Analysis Technique ◽

Modern Analysis

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

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Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

Advances in Mathematical Physics ◽

10.1155/2021/6616899 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Karim Guida ◽

Lahcen Ibnelazyz ◽

Khalid Hilal ◽

Said Melliani

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Differential Equations ◽

Existence And Uniqueness ◽

Uniqueness Of Solutions ◽

Krasnoselskii’S Fixed Point Theorem ◽

Existence And Uniqueness Results ◽

Uniqueness Results ◽

Fractional Differential ◽

Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

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