scholarly journals Nonlinear Impulsive Multi-Order Caputo-Type Generalized Fractional Differential Equations with Infinite Delay

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1108 ◽  
Author(s):  
Bashir Ahmad ◽  
Madeaha Alghanmi ◽  
Ahmed Alsaedi ◽  
Ravi P. Agarwal
Keyword(s):  
Contraction Mapping ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existence result is proved by means of Krasnoselskii’s fixed point theorem, while the contraction mapping principle is employed to obtain the uniqueness of solutions for the problem at hand. The paper concludes with illustrative examples.

scholarly journals Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Bashir Ahmad ◽  
Juan J. Nieto
Keyword(s):  
Differential Equation ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Nonlocal Boundary Value Problem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Differential

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional orderqgiven bycDqx(t)=f(t,x(t)),0<t<1,q∈(m−1,m],m∈ℕ,m≥2, x(0)=0, x′(0)=0, x′′(0)=0,…,x(m−2)(0)=0,x(1)=αx(η). Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.

scholarly journals Fractional order differential inclusions on an unbounded domain with infinite delay

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 167-178
Author(s):  
Mohamed Helal
Keyword(s):  
Fractional Order ◽  
Initial Value Problems ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Fréchet Spaces ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Hyperbolic Differential Inclusions

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

scholarly journals Nonlocal q-Symmetric Integral Boundary Value Problem for Sequential q-Symmetric Integrodifference Equations

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 218 ◽  
Author(s):  
Rujira Ouncharoen ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Value Problem ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Symmetric Integral

In this paper, we prove the sufficient conditions for the existence results of a solution of a nonlocal q-symmetric integral boundary value problem for a sequential q-symmetric integrodifference equation by using the Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Some examples are also presented to illustrate our results.

scholarly journals EXISTENCE AND STABILITY ANALYSIS OF SOLUTIONS FOR FRACTIONAL LANGEVIN EQUATION WITH NONLOCAL INTEGRAL AND ANTI-PERIODIC-TYPE BOUNDARY CONDITIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040006 ◽  
Author(s):  
AMITA DEVI ◽  
ANOOP KUMAR ◽  
THABET ABDELJAWAD ◽  
AZIZ KHAN
Keyword(s):  
Boundary Conditions ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Type Boundary ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

In this paper, we deal with the existence and uniqueness (EU) of solutions for nonlinear Langevin fractional differential equations (FDE) having fractional derivative of different orders with nonlocal integral and anti-periodic-type boundary conditions. Also, we investigate the Hyres–Ulam (HU) stability of solutions. The existence result is derived by applying Krasnoselskii’s fixed point theorem and the uniqueness of result is established by applying Banach contraction mapping principle. An example is offered to ensure the validity of our obtained results.

scholarly journals Study on the Existence of Solutions for a Class of Nonlinear Neutral Hadamard-Type Fractional Integro-Differential Equation with Infinite Delay

2021 ◽  
Vol 5 (2) ◽  
pp. 52
Author(s):  
Kaihong Zhao ◽  
Yue Ma
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Normed Space ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The existence of solutions for a class of nonlinear neutral Hadamard-type fractional integro-differential equations with infinite delay is researched in this paper. By constructing an appropriate normed space and utilizing the Banach contraction principle, Krasnoselskii’s fixed point theorem, we obtain some sufficient conditions for the existence of solutions. Finally, we provide an example to illustrate the validity of our main results.

scholarly journals Existence of Solutions for Integrodifferential Equations of Fractional Order with Antiperiodic Boundary Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Integrodifferential Equations ◽  
Krasnoselskii’S Fixed Point Theorem

We discuss the existence of solutions for a nonlinear antiperiodic boundary value problem of integrodifferential equations of fractional orderq∈(1,2]. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to establish the results.

Solvability of Anti-periodic BVPs for Impulsive Fractional Differential Systems Involving Caputo and Riemann–Liouville Fractional Derivatives

2018 ◽  
Vol 19 (2) ◽  
pp. 125-152 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Fixed Point ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential ◽  
Conclusion Section

AbstractSufficient conditions are given for the existence of solutions of anti-periodic value problems for impulsive fractional differential systems involving both Caputo and Riemann–Liouville fractional derivatives. We allow the nonlinearities$p(t)f(t,x,y,z,w)$and$q(t)g(t,x,y,z,w)$in fractional differential equations to be singular at$t=0$and$t=1$. Both$f$and$g$may be super-linear and sub-linear. The analysis relies on some well known fixed point theorems. The initial value problem discussed may be seen as a generalization of some ecological models. An example is given to illustrate the efficiency of the main theorems. Many unsuitable lemmas in recent published papers are pointed out in order not to mislead readers. A conclusion section is given at the end of the paper.

scholarly journals Existence of Solutions for Fractional Integro-Differential Equations with Non-Local Boundary Conditions

2018 ◽  
Vol 23 (3) ◽  
pp. 36 ◽  
Author(s):  
Hamed Bazgir ◽  
Bahman Ghazanfari
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Contraction Mapping ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Local Boundary ◽  
New Class ◽  
Non Local

In this paper, we study the existence of solutions for a new class of boundary value problems of non-linear fractional integro-differential equations. The existence result is obtained with the aid of Schauder type fixed point theorem while the uniqueness of solution is established by means of contraction mapping principle. Then, we present some examples to illustrate our results.

Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zahra Ahmadi ◽  
Rahmatollah Lashkaripour ◽  
Hamid Baghani ◽  
Shapour Heidarkhani
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Order Problem ◽  
Krasnoselskii’S Fixed Point Theorem

AbstractIn this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders $\gamma \in \left({n}_{1}-1,{n}_{1}\right]$ and $\eta \in \left({n}_{2}-1,{n}_{2}\right]$ for any ${n}_{1},{n}_{2}\in \mathrm{&#x2115;}$. We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and effectiveness.

scholarly journals Nonlocal Boundary Value Problems of Nonlinear Fractional (p,q)-Difference Equations

2021 ◽  
Vol 5 (4) ◽  
pp. 270
Author(s):  
Pheak Neang ◽  
Kamsing Nonlaopon ◽  
Jessada Tariboon ◽  
Sotiris K. Ntouyas ◽  
Bashir Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Given

In this paper, we study nonlinear fractional (p,q)-difference equations equipped with separated nonlocal boundary conditions. The existence of solutions for the given problem is proven by applying Krasnoselskii’s fixed-point theorem and the Leray–Schauder alternative. In contrast, the uniqueness of the solutions is established by employing Banach’s contraction mapping principle. Examples illustrating the main results are also presented.

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