scholarly journals On Holomorphic Solution for Space- and Time-Fractional Telegraph Equations in Complex Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Theoretical Result ◽  
Existence And Uniqueness ◽  
Complex Domain ◽  
Fractional Operators ◽  
Holomorphic Solution ◽  
Space And Time ◽  
Telegraph Equations

We consider some classes of space- and time-fractional telegraph equations in complex domain in sense of the Riemann-Liouville fractional operators for time and the Srivastava-Owa fractional operators for space. The existence and uniqueness of holomorphic solution are established. We illustrate our theoretical result by examples.

scholarly journals Ulam Stability for Fractional Differential Equation in Complex Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Complex Domain ◽  
Ulam Stability ◽  
Fractional Operators ◽  
Fractional Differential

The present paper deles with a fractional differential equationzαDzαu(z)+zu'(z)+(z2-a2)u(z)=∑n=0∞anzn+α,1<α≤2, wherez∈U:={z:|z|<1}in sense of Srivastava-Owa fractional operators. The existence and uniqueness of holomorphic solutions are established. Ulam stability for the approximation and holomorphic solutions are suggested.

scholarly journals An Aproximation to Solution of Space and Time Fractional Telegraph Equations by the Variational Iteration Method

2012 ◽  
Vol 2012 ◽  
pp. 1-2 ◽  
Author(s):  
Ji-Huan He
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Effective Algorithm ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations

Sevimlican suggested an effective algorithm for space and time fractional telegraph equations by the variational iteration method. This paper shows that algorithm can be updated by either variational iteration algorithm-II or the fractional variational iteration method.

scholarly journals Solution of the space-fractional telegraph equations by using HAM

2015 ◽  
Vol 37 ◽  
pp. 320
Author(s):  
Mehdi Abedi-Varaki ◽  
Shahram Rajabi ◽  
Vahid Ghorbani ◽  
Farzad Hosseinzadeh
Keyword(s):  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Space And Time ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Telegraph Equations

In this study by using the Homotopy Analysis Method (HAM) obtained approximate solutions for the space and time-fractional telegraph equations. In Caputo sense (Yildirim, 2010)these equations considered. Examples are solved and the obtained results show to be more accurate than Adomian Decomposition Method (ADM) and are more efficient and commodious.

scholarly journals SOME FURTHER EXTENSIONS CONSIDERING DISCRETE PROPORTIONAL FRACTIONAL OPERATORS

Fractals ◽  
2021 ◽  
pp. 2240026
Author(s):  
SAIMA RASHID ◽  
SOBIA SULTANA ◽  
YELIZ KARACA ◽  
AASMA KHALID ◽  
YU-MING CHU
Keyword(s):  
Fractional Calculus ◽  
Existence And Uniqueness ◽  
Complex Dynamics ◽  
Fractional Operator ◽  
Fractional Operators ◽  
Discrete Fractional Calculus ◽  
Dynamic Features ◽  
Fractional Difference ◽  
Fractional Systems ◽  
Special Cases

In this paper, some attempts have been devoted to investigating the dynamic features of discrete fractional calculus (DFC). To date, discrete fractional systems with complex dynamics have attracted the most consideration. By considering discrete [Formula: see text]-proportional fractional operator with nonlocal kernel, this study contributes to the major consequences of the certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete [Formula: see text]-proportional fractional sums, as presented. The proposed system has an intriguing feature not investigated in the literature so far, it is characterized by the nabla [Formula: see text] fractional sums. Novel special cases are reported with the intention of assessing the dynamics of the system, as well as to highlighting the several existing outcomes. In terms of applications, we can employ the derived consequences to investigate the existence and uniqueness of fractional difference equations underlying worth problems. Finally, the projected method is efficient in analyzing the complexity of the system.

scholarly journals Further results on existence of positive solutions of generalized fractional boundary value problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hojjat Afshari ◽  
Mohammed S. Abdo ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Operators ◽  
New Approach ◽  
Existence Of Positive Solutions ◽  
Contractive Type ◽  
Fractional Boundary Value Problems

Abstract This paper studies two classes of boundary value problems within the generalized Caputo fractional operators. By applying the fixed point result of α-ϕ-Geraghty contractive type mappings, we derive new results on the existence and uniqueness of the proposed problems. Illustrative examples are constructed to demonstrate the advantage of our results. The theorems reported not only provide a new approach but also generalize existing results in the literature.

scholarly journals Truth and justification for deductive systems: on the primary postulates and analyticity of justification

2019 ◽  
Vol 17 (4) ◽  
pp. 26-40
Author(s):  
Valentin N. Karpovich
Keyword(s):  
Existence And Uniqueness ◽  
A Priori ◽  
Definite Descriptions ◽  
Modern Logic ◽  
Traditional Logic ◽  
Deductive Systems ◽  
Space And Time ◽  
Synthetic A Priori

The concept of analyticity plays an important role in establishing truths. Both in the traditional logic of terms and modern logic of predicates, similar approaches are used to reconstruct the idea of reliable substantiation. Kant used the categories of synthetic a priori, Frege relied on the features of terms (individual constants and functions) to formulate the conditions for the application of definitions. As a result, primary statements as the beginning for substantiation presuppose the existence and uniqueness of a defined subject (definite descriptions), similar to the localization of objects in space and time by Kant’s synthetic apriori judgments.

scholarly journals Recent Fixed-Point Results for θ − Contraction Mappings in Rectangular M − Metric Spaces with Supportive Application

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mustafa Mudhesh ◽  
Hasanen A. Hammad ◽  
Habes Alsamir ◽  
Muhammad Arshad ◽  
Eskandar Ameer
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Theoretical Result ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Nonlinear Integral Equation ◽  
Metric Spaces ◽  
Contraction Mappings ◽  
Uniqueness Of The Solution

The goal of this manuscript is to present a new fixed-point theorem on θ − contraction mappings in the setting of rectangular M-metric spaces (RMMSs). Also, a nontrivial example to illustrate our main result has been given. Moreover, some related sequences with θ − contraction mappings have been discussed. Ultimately, our theoretical result has been implicated to study the existence and uniqueness of the solution to a nonlinear integral equation (NIE).

scholarly journals Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia

2021 ◽  
Author(s):  
Abdon Atangana ◽  
Seda IGRET ARAZ
Keyword(s):  
Infectious Disease ◽  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Integral Operators ◽  
Stochastic Approach ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Clear Indication

Several collected data representing the spread of some infectious disease have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish ‡u and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns. A clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely, the idea was first in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature. Keywords: Piecewise modeling, piecewise existence and uniqueness, piecewise numerical scheme, Covid-19 model, fractional operators and stochastic approach.

scholarly journals An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Sevimlican
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Space And Time ◽  
Telegraph Equations ◽  
He’S Variational Iteration Method

He's variational iteration method (VIM) is used for solving space and time fractional telegraph equations. Numerical examples are presented in this paper. The obtained results show that VIM is effective and convenient.

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