SOLVABILITY FOR A CLASS OF NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR IN BANACH SPACES

This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the Caputo-Hadamard fractional-order with $\mathrm{p}$-Laplacian operator in Banach spaces. The arguments are based on M\"{o}nch's fixed point theorem combined with the technique of measures of noncompactness. An example is also presented to illustrate the effectiveness of the main results.

Caputo-Hadamard fractional differential equations in banach spaces

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2018-0056 ◽

2018 ◽

Vol 21 (4) ◽

pp. 1027-1045 ◽

Cited By ~ 11

Author(s):

Saïd Abbas ◽

Mouffak Benchohra ◽

Naima Hamidi ◽

Johnny Henderson

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Banach Spaces ◽

Measure Of Noncompactness ◽

Existence Results ◽

Hadamard Fractional Differential Equations ◽

Mönch’S Fixed Point Theorem ◽

Abstract This article deals with some existence results for a class of Caputo–Hadamard fractional differential equations. The results are based on the Mönch’s fixed point theorem associated with the technique of measure of noncompactness. Two illustrative examples are presented.

Existence and Kummer Stability for a System of Nonlinear ϕ-Hilfer Fractional Differential Equations with Application

Fractal and Fractional ◽

10.3390/fractalfract5040200 ◽

2021 ◽

Vol 5 (4) ◽

pp. 200

Author(s):

Fatemeh Mottaghi ◽

Chenkuan Li ◽

Thabet Abdeljawad ◽

Reza Saadati ◽

Mohammad Bagher Ghaemi

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Point Theorem ◽

Existence Of Solutions ◽

Biological Systems ◽

Krasnoselskii’S Fixed Point Theorem ◽

Using Krasnoselskii’s fixed point theorem and Arzela–Ascoli theorem, we investigate the existence of solutions for a system of nonlinear ϕ-Hilfer fractional differential equations. Moreover, applying an alternative fixed point theorem due to Diaz and Margolis, we prove the Kummer stability of the system on the compact domains. We also apply our main results to study the existence and Kummer stability of Lotka–Volterra’s equations that are useful to describe and characterize the dynamics of biological systems.

Impulsive Fractional Differential Equations with p-Laplacian Operator in Banach Spaces

Journal of Function Spaces ◽

10.1155/2018/2503915 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Jingjing Tan ◽

Kemei Zhang ◽

Meixia Li

Keyword(s):

Differential Equations ◽

Banach Spaces ◽

Existence Of Solutions ◽

Sufficient Conditions ◽

Laplacian Operator ◽

Multiple Point ◽

Noncompactness Measure ◽

Fractional Differential ◽

Sadovskii Fixed Point Theorem

In this paper, we study a class of boundary value problem (BVP) with multiple point boundary conditions of impulsive p-Laplacian operator fractional differential equations. We establish the sufficient conditions for the existence of solutions in Banach spaces. Our analysis relies on the Kuratowski noncompactness measure and the Sadovskii fixed point theorem. An example is given to demonstrate the main results.

Solvability of initial value problems with fractional order differential equations in banach spaces by α-dense curves

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2017-0034 ◽

2017 ◽

Vol 20 (3) ◽

Cited By ~ 3

Author(s):

Gonzalo García

Keyword(s):

Differential Equation ◽

Banach Space ◽

Fixed Point ◽

Fixed Point Theorem ◽

Initial Value Problems ◽

Existence Of Solutions ◽

Initial Value ◽

Measures Of Noncompactness ◽

Fractional Order Differential Equations ◽

AbstractIn this paper we study the existence of solutions for an initial value problem, posed in a given Banach space, with a fractional differential equation via densifiability techniques. For our goal, we will prove a new fixed point result (not based on measures of noncompactness) which is, in forms, a generalization of the well-known Darbo’s fixed point theorem but essentially different. Some illustrative examples are given.

Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations withp-Laplacian Operator

Mathematical Problems in Engineering ◽

10.1155/2014/692703 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Ilkay Yaslan Karaca ◽

Fatma Tokmak

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Boundary Value Problem ◽

Fixed Point Theorems ◽

Nonlinear Boundary ◽

Existence Of Solutions ◽

Laplacian Operator ◽

Impulsive Fractional Differential Equations ◽

This paper studies the existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations withp-Laplacian operator. Our results are based on some standard fixed point theorems. Examples are given to show the applicability of our results.

Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Filomat ◽

10.2298/fil1705265f ◽

2017 ◽

Vol 31 (5) ◽

pp. 1265-1277 ◽

Cited By ~ 1

Author(s):

Fatma Fen ◽

Ilkay Karac ◽

Ozlem Ozen

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Boundary Value Problems ◽

Positive Solutions ◽

Point Theorem ◽

Laplacian Operator ◽

Existence Of Positive Solutions ◽

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions

Journal of Function Spaces ◽

10.1155/2020/4739175 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Jingli Xie ◽

Lijing Duan

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Existence Of Solutions ◽

Integral Boundary Conditions ◽

Laplacian Operator ◽

Integral Boundary ◽

Fractional Differential ◽

Integral Boundary Value Problems ◽

The Fixed Point Theorem

In this paper, we investigate a class of integral boundary value problems of fractional differential equations with a p-Laplacian operator. Existence of solutions is obtained by using the fixed point theorem, and an example is given to show the applicability of our main result.

Existence of solutions of nonlinear differential equations with deviating arguments

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700029968 ◽

1991 ◽

Vol 44 (3) ◽

pp. 467-476

Author(s):

K. Balachandran ◽

S. Ilamaran

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Existence Theorem ◽

Point Theorem ◽

Measure Of Noncompactness ◽

Existence Of Solutions ◽

Nonlinear Differential Equations ◽

Deviating Arguments ◽

Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

Solvability for a couple system of nonlinear fractional differential equations in a Banach space

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-013-0004-0 ◽

2013 ◽

Vol 16 (1) ◽

Cited By ~ 10

Author(s):

Jitai Liang ◽

Zhenhai Liu ◽

Xuhuan Wang

Keyword(s):

Banach Space ◽

Fixed Point ◽

Fixed Point Theorem ◽

Differential Equations ◽

Couple System ◽

Measures Of Noncompactness ◽

Nonlinear Fractional Differential Equations ◽

Fractional Differential ◽

The Fixed Point Theorem

AbstractIn this paper, we study boundary value problems of nonlinear fractional differential equations in a Banach Space E of the following form: $\left\{ \begin{gathered} D_{0^ + }^p x(t) = f_1 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ D_{0^ + }^q y(t) = f_2 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ x(0) + \lambda _1 x(1) = g_1 (x,y), \hfill \\ y(0) + \lambda _2 y(1) = g_2 (x,y), \hfill \\ \end{gathered} \right. $ where D 0+ denotes the Caputo fractional derivative, 0 < p,q ≤ 1. Some new results on the solutions are obtained, by the concept of measures of noncompactness and the fixed point theorem of Mönch type.

Multiple positive solutions for a system of $(p_{1}, p_{2}, p_{3})$-Laplacian Hadamard fractional order BVP with parameters

Advances in Difference Equations ◽

10.1186/s13662-021-03591-7 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sabbavarapu Nageswara Rao ◽

Abdullah Ali H. Ahmadini

Keyword(s):

Fixed Point ◽

Differential Equations ◽

Positive Solutions ◽

Fractional Order ◽

Fixed Point Theorems ◽

Laplacian Operator ◽

Multiple Positive Solutions ◽

Hadamard Fractional Differential Equations ◽

AbstractIn this article, we are pleased to investigate multiple positive solutions for a system of Hadamard fractional differential equations with $(p_{1}, p_{2}, p_{3})$ ( p 1 , p 2 , p 3 ) -Laplacian operator. The main results rely on the standard tools of different fixed point theorems. Finally, we demonstrate the application of the obtained results with the aid of examples.