scholarly journals Existence results and the dimension of the solution set for a nonlocal inclusions problem with mixed fractional derivatives and integrals

2020 ◽  
Vol 2020 (1) ◽  
Keyword(s):  
Fractional Derivatives ◽  
Existence Results ◽  
Solution Set ◽  
Fractional Derivatives And Integrals ◽  
Mixed Fractional Derivatives

scholarly journals A study on multiterm hybrid multi-order fractional boundary value problem coupled with its stability analysis of Ulam–Hyers type

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Nouara ◽  
Abdelkader Amara ◽  
Eva Kaslik ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Research Work ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Numerical Examples ◽  
Fractional Derivatives And Integrals ◽  
Fractional Differential

AbstractIn this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.

scholarly journals Nonlocal Fractional Hybrid Boundary Value Problems Involving Mixed Fractional Derivatives and Integrals via a Generalization of Darbo’s Theorem

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ayub Samadi ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problem ◽  
Theoretical Result ◽  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Boundary Value ◽  
Measures Of Noncompactness ◽  
Fractional Derivatives And Integrals ◽  
Mixed Fractional Derivatives

In this work, a new existence result is established for a nonlocal hybrid boundary value problem which contains one left Caputo and one right Riemann–Liouville fractional derivatives and integrals. The main result is proved by applying a new generalization of Darbo’s theorem associated with measures of noncompactness. Finally, an example to justify the theoretical result is also presented.

scholarly journals Existence Results for a Nonlocal Coupled System of Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 578
Author(s):  
Sotiris K. Ntouyas ◽  
Abrar Broom ◽  
Ahmed Alsaedi ◽  
Tareq Saeed ◽  
Bashir Ahmad
Keyword(s):  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Uniqueness Result ◽  
Existence Results ◽  
System Of Differential Equations ◽  
Liouville Type ◽  
Uniqueness Of Solutions ◽  
Fractional Derivatives And Integrals

In this paper, we study the existence and uniqueness of solutions for a new kind of nonlocal four-point fractional integro-differential system involving both left Caputo and right Riemann–Liouville fractional derivatives, and Riemann–Liouville type mixed integrals. The Banach and Schaefer fixed point theorems are used to obtain the desired results. An example illustrating the existence and uniqueness result is presented.

The properties of Bessel-type fractional derivatives and integrals

2016 ◽  
pp. 3973-3982
Author(s):  
V. R. Lakshmi Gorty
Keyword(s):  
Fractional Order ◽  
Real Line ◽  
Computer Algebra System ◽  
Fractional Derivatives ◽  
Graphical Representation ◽  
Fractional Integrals ◽  
The Real ◽  
Fractional Derivatives And Integrals ◽  
Half Axis ◽  
Derivatives Of

The fractional integrals of Bessel-type Fractional Integrals from left-sided and right-sided integrals of fractional order is established on finite and infinite interval of the real-line, half axis and real axis. The Bessel-type fractional derivatives are also established. The properties of Fractional derivatives and integrals are studied. The fractional derivatives of Bessel-type of fractional order on finite of the real-line are studied by graphical representation. Results are direct output of the computer algebra system coded from MATLAB R2011b.

scholarly journals Positive solutions for a system of fractional differential equations with p-Laplacian operator and multi-point boundary conditions

2018 ◽  
Vol 23 (5) ◽  
pp. 771-801 ◽  
Author(s):  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Existence Results ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

>We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann–Liouville fractional differential equations with parameters and p-Laplacian operator subject to multi-point boundary conditions, which contain fractional derivatives. The proof of our main existence results is based on the Guo–Krasnosel'skii fixed-point theorem.

Fractional Order Derivative and Integral Computation with a Small Number of Discrete Input Values Using Grünwald–Letnikov Formula

2019 ◽  
Vol 17 (05) ◽  
pp. 1940006
Author(s):  
Dariusz W. Brzeziński
Keyword(s):  
Input Data ◽  
Fractional Derivatives ◽  
Difficult Problem ◽  
Computational Method ◽  
Problem Solution ◽  
Fractional Derivatives And Integrals ◽  
Discrete Values ◽  
Arbitrary Precision ◽  
Modern Programming Language ◽  
Accuracy Of Approximation

High-accuracy computer approximation of fractional derivatives and integrals by applying Grünwald–Letnikov formula generally requires a large number of input values. If required amount cannot be supplied, accuracy of approximation drops drastically. In this paper, we solve a difficult problem in this scope, i.e., when input data consists only of a small number of discrete values. Furthermore, some of the values may be unusable for computational purposes. Our problem solution includes an appropriate method of input data preprocessing, an interpolation algorithm with extrapolation abilities, a central point function discretization schema, recurrent computational method of coefficients and application of Horner’s schema for the core of the Grünwald–Letnikov method: coefficients and function’s values multiplication. Numerical method presented in the paper enables to compute fractional derivatives and integrals of complicated functions with much higher accuracy than it is possible when application of the default approach to Grünwald–Letnikov method computer implementation is applied. This new method usually takes only 10% of function’s values required by the default approach for the same computations and is much less restrictive for their quality. The general novelty of the method is an efficient configuration of existing numerical methods and enhancement of their abilities by applying modern programming language — Python and arbitrary precision arithmetic for computations.

scholarly journals Desiderata for Fractional Derivatives and Integrals

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 149 ◽  
Author(s):  
Rudolf Hilfer ◽  
Yuri Luchko
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Fractional Integral ◽  
Special Issue ◽  
Fractional Derivatives And Integrals

The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are neither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend to stimulate the field by providing guidelines based on a small number of time honoured and well established criteria.

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