scholarly journals Analytical Study of Two Nonlinear Coupled Hybrid Systems Involving Generalized Hilfer Fractional Operators

2021 ◽  
Vol 5 (4) ◽  
pp. 178
Author(s):  
Mohammed A. Almalahi ◽  
Omar Bazighifan ◽  
Satish K. Panchal ◽  
S. S. Askar ◽  
Georgia Irina Oros
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Analytical Study ◽  
Sufficient Conditions ◽  
Coupled Systems ◽  
Krasnoselskii Fixed Point Theorem ◽  
Hybrid Fixed Point Theorem ◽  
Fractional Differential

In this research paper, we dedicate our interest to an investigation of the sufficient conditions for the existence of solutions of two new types of a coupled systems of hybrid fractional differential equations involving ϕ-Hilfer fractional derivatives. The existence results are established in the weighted space of functions using Dhage’s hybrid fixed point theorem for three operators in a Banach algebra and Dhage’s helpful generalization of Krasnoselskii fixed- point theorem. Finally, simulated examples are provided to demonstrate the obtained results.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses

2019 ◽  
Vol 22 (2) ◽  
pp. 495-508 ◽  
Author(s):  
Jayanta Borah ◽  
Swaroop Nandan Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Mild Solution ◽  
Point Theorem ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Fractional Order Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

Abstract In this article, we establish a set of sufficient conditions for the existence of mild solution of a class of fractional differential equations with not instantaneous impulses. The results are obtained by using Banach fixed point theorem and Krasnoselskii’s fixed point theorem. An example is presented for validation of result.

scholarly journals A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Xiangbing Zhou ◽  
Wenquan Wu ◽  
Hongjiang Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010). We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.

scholarly journals Existence of Positive Solutions for a Class of Delay Fractional Differential Equations with Generalization to N-Term

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Initial Conditions ◽  
Banach Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We established the existence of a positive solution of nonlinear fractional differential equationsL(D)[x(t)−x(0)]=f(t,xt),t∈(0,b]with finite delayx(t)=ω(t),t∈[−τ,0], wherelimt→0f(t,xt)=+∞, that is,fis singular att=0andxt∈C([−τ,0],ℝ≥0). The operator ofL(D)involves the Riemann-Liouville fractional derivatives. In this problem, the initial conditions with fractional order and some relations among them were considered. The analysis rely on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point theorem, and the Arzela-Ascoli theorem in a cone.

scholarly journals Positive Solutions for a Higher-Order Semipositone Nonlocal Fractional Differential Equation with Singularities on Both Time and Space Variable

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Kemei Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equation ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Space Variable ◽  
Higher Order ◽  
Existence Results ◽  
Fractional Differential

In this paper, we consider the following higher-order semipositone nonlocal Riemann-Liouville fractional differential equation D0+αx(t)+f(t,x(t),D0+βx(t))+e(t)=0,  0<t<1,D0+βx(0)=D0+β+1x(0)=⋯=D0+n+β-2x(0)=0, and D0+βx(1)=∑i=1m-2ηiD0+βx(ξi), where D0+α and D0+β are the standard Riemann-Liouville fractional derivatives. The existence results of positive solution are given by Guo-krasnosel’skii fixed point theorem and Schauder’s fixed point theorem.

scholarly journals Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Mohamed Hannabou ◽  
Hilal Khalid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Coupled Systems ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

The study of coupled systems of hybrid fractional differential equations requires the attention of scientists for the exploration of their different important aspects. Our aim in this paper is to study the existence and uniqueness of the solution for impulsive hybrid fractional differential equations. The novelty of this work is the study of a coupled system of impulsive hybrid fractional differential equations with initial and boundary hybrid conditions. We used the classical fixed-point theorems such as the Banach fixed-point theorem and Leray–Schauder alternative fixed-point theorem for existence results. We also give an example of the main results.

scholarly journals Ulam Type Stability for a Coupled System of Boundary Value Problems of Nonlinear Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Aziz Khan ◽  
Kamal Shah ◽  
Yongjin Li ◽  
Tahir Saeed Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Generalized Metric Space ◽  
Ulam Stability ◽  
Fractional Differential ◽  
Necessary And Sufficient

We discuss existence, uniqueness, and Hyers-Ulam stability of solutions for coupled nonlinear fractional order differential equations (FODEs) with boundary conditions. Using generalized metric space, we obtain some relaxed conditions for uniqueness of positive solutions for the mentioned problem by using Perov’s fixed point theorem. Moreover, necessary and sufficient conditions are obtained for existence of at least one solution by Leray-Schauder-type fixed point theorem. Further, we also develop some conditions for Hyers-Ulam stability. To demonstrate our main result, we provide a proper example.

scholarly journals On the controllability of Hilfer-Katugampola fractional differential equations

2020 ◽  
Vol 24 (2) ◽  
pp. 195-204
Author(s):  
Mohamed I. Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Sufficient Conditions ◽  
Fractional Differential

By employing Kuratowski's measure of noncompactness together with Sadovskii's fixed point theorem, sufficient conditions for controllability results of Hilfer-Katugampola fractional differential equations in Banach spaces are derived.

scholarly journals On Caputo–Hadamard type coupled systems of nonconvex fractional differential inclusions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samiha Belmor ◽  
Fahd Jarad ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Fractional Differential Inclusions ◽  
Research Article ◽  
Fractional Differential

AbstractThis research article is mainly concerned with the existence of solutions for a coupled Caputo–Hadamard of nonconvex fractional differential inclusions equipped with boundary conditions. We derive our main result by applying Mizoguchi–Takahashi’s fixed point theorem with the help of $\mathcal{P}$ P -function characterizations.

On the behavior of solutions of fractional differential equations on time scale via Hilfer fractional derivatives

2018 ◽  
Vol 21 (4) ◽  
pp. 1120-1138 ◽  
Author(s):  
Devaraj Vivek ◽  
Kuppusamy Kanagarajan ◽  
Seenith Sivasundaram
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Existence And Stability ◽  
Fractional Differential

Abstract In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results.

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