scholarly journals Nonlocal Initial Value Problem for Hybrid Generalized Hilfer-type Fractional Implicit Differential Equations

2021 ◽  
Vol 8 (1) ◽  
pp. 87-100
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
Jamal Eddine Lazreg ◽  
Juan J. Nieto ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Banach Algebras ◽  
Existence Results ◽  
Initial Value ◽  
Hilfer Fractional Derivative ◽  
Implicit Differential Equations

Abstract In this paper, we prove some existence results of solutions for a class of nonlocal initial value problem for nonlinear fractional hybrid implicit differential equations under generalized Hilfer fractional derivative. The result is based on a fixed point theorem on Banach algebras. Further, examples are provided to illustrate our results.

L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Benoumran Telli ◽  
Mohammed Said Souid
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Initial Value Problems ◽  
Initial Value ◽  
Hadamard Fractional Derivative ◽  
Implicit Differential Equations ◽  
Banach Contraction

Abstract In this paper, we study the existence of integrable solutions for initial value problems for fractional order implicit differential equations with Hadamard fractional derivative. Our results are based on Schauder’s fixed point theorem and the Banach contraction principle fixed point theorem.

Existence theory of fractional coupled differential equations via Ψ-Hilfer fractional derivative

2019 ◽  
Vol 27 (4) ◽  
pp. 207-212 ◽  
Author(s):  
Sugumaran Harikrishnan ◽  
Kamal Shah ◽  
Kuppusamy Kanagarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Point Theorem ◽  
Existence Results ◽  
Existence Theory ◽  
Hilfer Fractional Derivative ◽  
Coupled Differential Equations ◽  
Schaefer Fixed Point Theorem

Abstract In this paper, we analyze existence results for coupled differential equations via ψ- Hilfer fractional derivative. The proof relies on the Schaefer fixed point theorem.

scholarly journals Existence of Mild Solutions for a Class of Impulsive Hilfer Fractional Coupled Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Karim Guida ◽  
Khalid Hilal ◽  
Lahcen Ibnelazyz ◽  
Ming Mei
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Derivative ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Existence Results ◽  
Coupled Systems ◽  
Hilfer Fractional Derivative

The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem.

scholarly journals Existence Results for the Distributed Order Fractional Hybrid Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Hossein Noroozi ◽  
Alireza Ansari ◽  
Mohammad Shafi Dahaghin
Keyword(s):  
Fixed Point ◽  
Differential Operator ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Banach Algebras ◽  
Existence Results ◽  
Carathéodory Conditions ◽  
Distributed Order ◽  
Hybrid Differential Equations

We introduce the distributed order fractional hybrid differential equations (DOFHDEs) involving the Riemann-Liouville differential operator of order0<q<1with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved via a fixed point theorem in the Banach algebras under the mixed Lipschitz and Caratheodory conditions.

Initial Value Problem of Fractional Integro-Differential Equations in Banach Space

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Adel Jawahdou
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Initial Value Problem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Initial Value

AbstractThis paper is devoted to study the existence of solutions of nonlinear fractional integro-differential equation, via the techniques of measure of noncompactness. The investigation is based on a Schauder's fixed point theorem. The main result is less restrictive than those given in the literature. An illustrative example is given.

scholarly journals Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Saowaluck Chasreechai ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Existence Results ◽  
Initial Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Hybrid Fixed Point Theorem

We consider a hybrid fractional sum-difference initial value problem and a hybrid fractional sequential sum-difference initial value problem. The existence results of these two problems are proved by using the hybrid fixed point theorem for three operators in a Banach algebra and the generalized Krasnoselskii’s fixed point theorem, respectively.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

scholarly journals Existence results for second order functional differential and integrodifferential inclusions in Banach spaces

2001 ◽  
Vol 32 (4) ◽  
pp. 315-325
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Initial Value Problems ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Second Order ◽  
Initial Value ◽  
Functional Differential ◽  
Condensing Maps

In this paper we investigate the existence of solutions on a compact interval to second order initial value problems for functional differential and integrodifferential inclusions in Banach spaces. We shall make use of a fixed point theorem for condensing maps due to Martelli.

Initial value problem for hybrid $$\psi $$-Hilfer fractional implicit differential equations

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Abdelkrim Salim ◽  
Mouffak Benchohra ◽  
John R. Graef ◽  
Jamal Eddine Lazreg
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Initial Value ◽  
Implicit Differential Equations
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