scholarly journals A New technique of Initial Boundary Value Problems Using Homotopy Analysis Method

2017 ◽  
Vol 916 ◽  
pp. 012039
Author(s):  
D. M. Wang ◽  
W. Zhang ◽  
M. H. Yao ◽  
Y.L. Liu
Keyword(s):  
Boundary Value Problems ◽  
Homotopy Analysis Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
New Technique ◽  
Initial Boundary Value Problems ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
A New Technique ◽  
Initial Boundary Value

scholarly journals Homotopy Analysis Method for a Fractional Order Equation with Dirichlet and Non-Local Integral Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1167
Author(s):  
Said Mesloub ◽  
Saleem Obaidat
Keyword(s):  
Fractional Order ◽  
Homotopy Analysis Method ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Uniqueness Of The Solution ◽  
Non Local ◽  
Initial Boundary Value

The main purpose of this paper is to obtain some numerical results via the homotopy analysis method for an initial-boundary value problem for a fractional order diffusion equation with a non-local constraint of integral type. Some examples are provided to illustrate the efficiency of the homotopy analysis method (HAM) in solving non-local time-fractional order initial-boundary value problems. We also give some improvements for the proof of the existence and uniqueness of the solution in a fractional Sobolev space.

scholarly journals Blowing-up solutions of the time-fractional dispersive equations

2021 ◽  
Vol 10 (1) ◽  
pp. 952-971
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Berikbol T. Torebek
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Nonlinear Capacity ◽  
Blowing Up ◽  
De Vries ◽  
Initial Boundary Value

Abstract This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.

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