scholarly journals Existence and U-H-R Stability of Solutions to the Implicit Nonlinear FBVP in the Variable Order Settings

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1693
Author(s):  
Mohammed K. A. Kaabar ◽  
Ahmed Refice ◽  
Mohammed Said Souid ◽  
Francisco Martínez ◽  
Sina Etemad ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential ◽  
Existence Criteria

In this paper, the existence of the solution and its stability to the fractional boundary value problem (FBVP) were investigated for an implicit nonlinear fractional differential equation (VOFDE) of variable order. All existence criteria of the solutions in our establishments were derived via Krasnoselskii’s fixed point theorem and in the sequel, and its Ulam–Hyers–Rassias (U-H-R) stability is checked. An illustrative example is presented at the end of this paper to validate our findings.

scholarly journals Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqing Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.

scholarly journals Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jun-Rui Yue ◽  
Jian-Ping Sun ◽  
Shuqin Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fractional Differential

We consider the following boundary value problem of nonlinear fractional differential equation:(CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, whereα∈(2,3]is a real number, CD0+αdenotes the standard Caputo fractional derivative, andf:[0,1]×[0,+∞)→[0,+∞)is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.

scholarly journals Implicit Hybrid Fractional Boundary Value Problem via Generalized Hilfer Derivative

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1937
Author(s):  
Abdellatif ‬Boutiara ◽  
Mohammed S. ‬Abdo ◽  
Mohammed A. ‬Almalahi ◽  
Hijaz Ahmad ◽  
Amira Ishan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Algebras ◽  
Fractional Operators ◽  
Fractional Boundary Value Problem ◽  
Fractional Differential

This research paper is dedicated to the study of a class of boundary value problems for a nonlinear, implicit, hybrid, fractional, differential equation, supplemented with boundary conditions involving general fractional derivatives, known as the ϑ-Hilfer and ϑ-Riemann–Liouville fractional operators. The existence of solutions to the mentioned problem is obtained by some auxiliary conditions and applied Dhage’s fixed point theorem on Banach algebras. The considered problem covers some symmetry cases, with respect to a ϑ function. Moreover, we present a pertinent example to corroborate the reported results.

Existence of positive solutions for systems of nonlinear fractional differential equation with p-Laplacian

2019 ◽  
Vol 13 (05) ◽  
pp. 2050089 ◽  
Author(s):  
S. Nageswara Rao ◽  
Meshari Alesemi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we establish sufficient conditions for the existence of positive solutions for a system of nonlinear fractional [Formula: see text]-Laplacian boundary value problems under different combinations of superlinearity and sublinearity of the nonlinearities via the Guo–Krasnosel’skii fixed point theorem. Moreover, an example is given to illustrate our results.

scholarly journals Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Nonexistence ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0,where2<α<3is a real number andD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

scholarly journals The Ulam Stability of Fractional Differential Equation with the Caputo-Fabrizio Derivative

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Author(s):  
Shuyi Wang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Differential Equation ◽  
Point Theorem ◽  
Ulam Stability ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Uniqueness Results ◽  
Fractional Differential

The aim of this paper is to establish the Ulam stability of the Caputo-Fabrizio fractional differential equation with integral boundary condition. We also present the existence and uniqueness results of the solution for the Caputo-Fabrizio fractional differential equation by Krasnoselskii’s fixed point theorem and Banach fixed point theorem. Some examples are provided to illustrate our theorems.

Attractivity for differential equations of fractional order and ψ-Hilfer type

2020 ◽  
Vol 23 (4) ◽  
pp. 1188-1207
Author(s):  
J. Vanterler da C. Sousa ◽  
Mouffak Benchohra ◽  
Gaston M. N’Guérékata
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Derivatives ◽  
Broad Class ◽  
Hilfer Fractional Derivative ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

AbstractThis paper investigates the overall solution attractivity of the fractional differential equation involving the ψ-Hilfer fractional derivative and using the Krasnoselskii’s fixed point theorem. We highlight some particular cases of the results presented here, especially involving the Riemann-Liouville, thus illustrating the broad class of fractional derivatives to which these results can be applied.

Existence result for nonlinear fractional differential equations with nonlocal fractional integro-differential boundary conditions in Banach spaces

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Djamila Seba ◽  
Hamza Rebai ◽  
Johnny Henderson
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
Nonlinear Fractional Differential Equation ◽  
Measures Of Noncompactness ◽  
Fractional Differential

Abstract The nonlinear fractional differential equation with nonlocal fractional integro-differential boundary conditions in Banach spaces is studied, an existence result is obtained by using the method associated with the technique of measures of noncompactness and an appropriate fixed point theorem. An example is given to illustrate the theory.

scholarly journals A Study on the Solutions of a Multiterm FBVP of Variable Order

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zoubida Bouazza ◽  
Sina Etemad ◽  
Mohammed Said Souid ◽  
Shahram Rezapour ◽  
Francisco Martínez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Research Study ◽  
Existence Of Solution ◽  
Variable Order ◽  
Order Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

In the present research study, for a given multiterm boundary value problem (BVP) involving the nonlinear fractional differential equation (NnLFDEq) of variable order, the uniqueness-existence properties are analyzed. To arrive at such an aim, we first investigate some specifications of this kind of variable order operator and then derive required criteria confirming the existence of solution. All results in this study are established with the help of two fixed-point theorems and examined by a practical example.

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