scholarly journals Exact solutions of the Laplace fractional boundary value problems via natural decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1178-1187
Author(s):  
Hajira ◽  
Hassan Khan ◽  
Yu-Ming Chu ◽  
Rasool Shah ◽  
Dumitru Baleanu ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Boundary Value Problems ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Simple Procedure ◽  
Boundary Value ◽  
Decomposition Technique ◽  
Approximate Analytical Solutions ◽  
Natural Decomposition ◽  
Fractional Boundary Value Problems

Abstract In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs.

Exact Solutions for a Class of Nonlinear Singular Two-Point Boundary Value Problems: The Decomposition Method

2010 ◽  
Vol 65 (3) ◽  
pp. 145-150 ◽  
Author(s):  
Abd Elhalim Ebaid
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Boundary Value Problems ◽  
Decomposition Method ◽  
Applied Mathematics ◽  
Boundary Value ◽  
Adomian Decomposition Method ◽  
Point Boundary ◽  
Adomian Decomposition ◽  
First Time

Many problems in applied mathematics and engineering are usually formulated as singular two-point boundary value problems. A well-known fact is that the exact solutions in closed form of such problems were not obtained in many cases. In this paper, the exact solutions for a class of nonlinear singular two-point boundary value problems are obtained to the first time by using Adomian decomposition method

An inhomogeneous problem for an elastic half-strip: An exact solution

2021 ◽  
pp. 108128652199641
Author(s):  
Mikhail D Kovalenko ◽  
Irina V Menshova ◽  
Alexander P Kerzhaev ◽  
Guangming Yu
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Theory Of Elasticity ◽  
Orthogonality Relation ◽  
Infinite Strip ◽  
Inhomogeneous Problem ◽  
Half Strip

We construct exact solutions of two inhomogeneous boundary value problems in the theory of elasticity for a half-strip with free long sides in the form of series in Papkovich–Fadle eigenfunctions: (a) the half-strip end is free and (b) the half-strip end is firmly clamped. Initially, we construct a solution of the inhomogeneous problem for an infinite strip. Subsequently, the corresponding solutions for a half-strip are added to this solution, whereby the boundary conditions at the end are satisfied. The Papkovich orthogonality relation is used to solve the inhomogeneous problem in a strip.

scholarly journals Existence and uniqueness criteria for the higher-order Hilfer fractional boundary value problems at resonance

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yousef Gholami
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Higher Order ◽  
Coupled Systems ◽  
At Resonance ◽  
Uniqueness Criteria ◽  
Fractional Boundary Value Problems

Abstract This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative application.

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