A unique solution for the exact differential equation of nonuniform lines

1968 ◽  
Vol 56 (12) ◽  
pp. 2181-2182 ◽  
Author(s):  
A.G.J. Holt ◽  
K.U. Ahmed
Keyword(s):  
Differential Equation ◽  
Unique Solution

scholarly journals Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 851
Author(s):  
Robert Stegliński
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Weak Solution ◽  
Variational Methods ◽  
Unique Solution ◽  
Continuous Dependence ◽  
Fractional Laplacian ◽  
Unique Weak Solution ◽  
Fractional Partial Differential Equation ◽  
Integrodifferential Operator

In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods.

scholarly journals The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System’s Co-Evolution Process

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Teng Ren ◽  
Helu Xiao ◽  
Zhongbao Zhou ◽  
Xinguang Zhang ◽  
Lining Xing ◽  
...  
Keyword(s):  
Differential Equation ◽  
Convergence Analysis ◽  
Unique Solution ◽  
Fractional Differential Equation ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Singular Fractional Differential Equation ◽  
Complex Processes ◽  
Fractional Differential ◽  
And Diffusion

In this paper, we focus on a class of singular fractional differential equation, which arises from many complex processes such as the phenomenon and diffusion interaction of the ecological-economic-social complex system. By means of the iterative technique, the uniqueness and nonexistence results of positive solutions are established under the condition concerning the spectral radius of the relevant linear operator. In addition, the iterative scheme that converges to the unique solution is constructed without request of any monotonicity, and the convergence analysis and error estimate of unique solution are obtained. The numerical example and simulation are also given to demonstrate the application of the main results and the effectiveness of iterative process.

scholarly journals L -Simulation Functions over b -Metric-Like Spaces and Fractional Hybrid Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Shimaa I. Moustafa ◽  
Ayman Shehata
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Unique Solution ◽  
Caputo Fractional Derivative ◽  
Multipoint Boundary Conditions ◽  
Simulation Functions ◽  
Hybrid Differential Equation ◽  
Hybrid Differential Equations

In this paper, we establish some fixed point results for α q s p -admissible mappings embedded in L -simulation functions in the context of b -metric-like spaces. As an application, we discuss the existence of a unique solution for fractional hybrid differential equation with multipoint boundary conditions via Caputo fractional derivative of order 1 < α ≤ 2 . Some examples and corollaries are also considered to illustrate the obtained results.

Univalent Solutions of W″ + pW = 0

1962 ◽  
Vol 14 ◽  
pp. 69-78 ◽  
Author(s):  
R. K. Brown
Keyword(s):  
Differential Equation ◽  
Unique Solution ◽  
Image Position ◽  
Indicial Equation

Consider the differential equation1.1where1.2is regular in |z| < R.The indicial equation associated with (1.1) is of the formWe shall denote the two roots of this equation by α and β, where . Corresponding to the root α there exists a unique solution of (1.1) of the following form1.3In those cases for which there exists a unique second solution of (1.1) of the form1.4

scholarly journals A Refinement of Quasilinearization Method for Caputo's Sense Fractional-Order Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Coşkun Yakar ◽  
Ali Yakar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Unique Solution ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Quasilinearization Method ◽  
Fractional Order Differential Equation ◽  
Fractional Order Differential Equations ◽  
Quasilinearization Technique

The method of the quasilinearization technique in Caputo's sense fractional-order differential equation is applied to obtain lower and upper sequences in terms of the solutions of linear Caputo's sense fractional-order differential equations. It is also shown that these sequences converge to the unique solution of the nonlinear Caputo's sense fractional-order differential equation uniformly and semiquadratically with less restrictive assumptions.

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