scholarly journals Boundary Value Problem for Fractional Order Generalized Hilfer-Type Fractional Derivative with Non-Instantaneous Impulses

2020 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
John R. Graef ◽  
Jamal Eddine Lazreg
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Differential ◽  
Krasnosel’Skii’S Fixed Point Theorem ◽  
Banach’S Contraction Principle ◽  
Implicit Fractional Differential Equations

This manuscript is devoted to proving some results concerning the existence of solutions to a class of boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer fractional derivatives. The results are based on Banach’s contraction principle and Krasnosel’skii’s fixed point theorem. To illustrate the results, an example is provided.

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.

scholarly journals Study of fractional order pantograph type impulsive antiperiodic boundary value problem

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Arshad Ali ◽  
Kamal Shah ◽  
Thabet Abdeljawad ◽  
Hasib Khan ◽  
Aziz Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Boundary Value ◽  
Impulsive Conditions ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Stability Results ◽  
Implicit Fractional Differential Equations

Abstract In this paper, we study existence and stability results of an anti-periodic boundary value problem of nonlinear delay (pantograph) type implicit fractional differential equations with impulsive conditions. Using Schaefer’s fixed point theorem and Banach’s fixed point theorem, we have established results of at least one solution and uniqueness. Also, using the Hyers–Ulam concept, we have derived various kinds of Ulam stability results for the considered problem. Finally, we have applied our obtained results to a numerical problem.

scholarly journals Boundary Value Problem for ψ-Caputo Fractional Differential Equations in Banach Spaces via Densifiability Techniques

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 153
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

A novel fixed-point theorem based on the degree of nondensifiability (DND) is used in this article to examine the existence of solutions to a boundary value problem containing the ψ-Caputo fractional derivative in Banach spaces. Besides that, an example is included to verify our main results. Moreover, the outcomes obtained in this research paper ameliorate and expand some previous findings in this area.

scholarly journals Fiedler vector analysis for particular cases of connected graphs

2021 ◽  
Vol 40 (4) ◽  
pp. 1041-1051
Author(s):  
Daniel Felisberto Traciná Filho ◽  
Claudia Marcela Justel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Lyapunov Inequality ◽  
Laplacian Eigenvalue ◽  
Fiedler Vector

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.

scholarly journals Existence of Positive Solution for the Eighth-Order Boundary Value Problem Using Classical Version of Leray–Schauder Alternative Fixed Point Theorem

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 129 ◽  
Author(s):  
Thenmozhi Shanmugam ◽  
Marudai Muthiah ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Eighth Order ◽  
Classical Version ◽  
Nonlinear Alternative

In this work, we investigate the existence of solutions for the particular type of the eighth-order boundary value problem. We prove our results using classical version of Leray–Schauder nonlinear alternative fixed point theorem. Also we produce a few examples to illustrate our results.

scholarly journals The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yuanyuan Pan ◽  
Zhenlai Han ◽  
Shurong Sun ◽  
Yige Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Continuous Functions ◽  
Fractional Boundary Value Problems ◽  
Schäuder Fixed Point Theorem

We study the existence of solutions for the boundary value problem-Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)),-Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)),y1(ν-2)=Δy1(ν+b)=0,y2(μ-2)=Δy2(μ+b)=0, where1<μ,ν≤2,f,g:R×R→Rare continuous functions,b∈N0. The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.

Existence of positive solutions for a class of fractional differential equation systems with multi-point boundary conditions

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Hussian Akrami ◽  
Gholam Hussian Erjaee
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence Of Solutions ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractIn this article, we study the existence of positive solutions of a multi-point boundary value problem for some system of fractional differential equations. The fixed point theorem on cones will be applied to demonstrate the existence of solutions for this system. At the end, an example shows the application of the main results.

scholarly journals Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
S. Nageswara Rao ◽  
M. Zico Meetei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Coupled System ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

In this paper, we consider a four-point coupled boundary value problem for system of the nonlinear semipositone fractional differential equation D0+αu(t)+λf(t,u(t),v(t))=0,  0<t<1, D0+αv(t)+μg(t,u(t),v(t))=0,  0<t<1, u(0)=v(0)=0,  a1D0+βu(1)=b1D0+βv(ξ), a2D0+βv(1)=b2D0+βu(η),  η,ξ∈(0,1), where the coefficients ai,bi,i=1,2 are real positive constants, α∈(1,2],β∈(0,1],D0+α, D0+β are the standard Riemann-Liouville derivatives. Values of the parameters λ and μ are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone.

L 1-solutions of the boundary value problem for implicit fractional order differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Banach Contraction ◽  
The Banach Contraction Principle

Abstract The aim of this paper is to present new results on the existence of solutions for a class of the boundary value problem for fractional order implicit differential equations involving the Caputo fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

scholarly journals Lyapunov-type inequality for higher order left and right fractional p-Laplacian problems

2021 ◽  
Vol 40 (4) ◽  
pp. 1031-1040
Author(s):  
Alberto Cabada ◽  
Rabah Khaldi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Type Inequality ◽  
Lyapunov Inequality ◽  
Laplacian Eigenvalue ◽  
Left And Right ◽  
Lyapunov Type Inequality

In this paper, we consider a p-Laplacian eigenvalue boundary value problem involving both right Caputo and left Riemann-Liouville types fractional derivatives. To prove the existence of solutions, we apply the Schaefer’s fixed point theorem. Furthermore, we present the Lyapunov inequality for the corresponding problem.

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