scholarly journals Non-Oscillating solutions of a generalized system of ODEs with derivative terms

2021 ◽  
Vol 8 (1) ◽  
pp. 239-250
Author(s):  
B V K Bharadwaj ◽  
Pallav Kumar Baruah
Keyword(s):  
Fixed Point ◽  
Linear Function ◽  
Existence Of A Solution ◽  
Generalized System ◽  
Oscillating Solutions ◽  
Mixed Order ◽  
Non Linear ◽  
Fixed Point Technique

Abstract We consider a system of ODEs of mixed order with derivative terms appearing in the non-linear function and show the existence of a solution which does not oscillate for such system. We applied the fixed point technique to show that under certain conditions there exists at least one solution to the system which is not only non-oscillating, but also asymptotically constant.

scholarly journals A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 206 ◽  
Author(s):  
Sumati Panda ◽  
Asifa Tassaddiq ◽  
Ravi Agarwal
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Efficient Solution ◽  
New Approach ◽  
Non Linear ◽  
Fixed Point Technique ◽  
Linear Integral ◽  
Linear Integral Equations

In this article, we introduce and establish various approaches related to the F-contraction using new sorts of contractions, namely the extended F B e -contraction, the extended F B e -expanding contraction, and the extended generalized F B e -contraction. Thereafter, we propose a simple and efficient solution for non-linear integral equations using the fixed point technique in the setting of a B e -metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples where necessary.

scholarly journals General algorithm and sensitivity analysis for variational inequalities

1992 ◽  
Vol 5 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Sensitivity Analysis ◽  
Fixed Point ◽  
Variational Inequalities ◽  
Complementarity Problems ◽  
General Algorithm ◽  
Projection Technique ◽  
Existence Of A Solution ◽  
Odd Order ◽  
Special Cases ◽  
Fixed Point Technique

The fixed point technique is used to prove the existence of a solution for a class of variational inequalities related to odd order boundary value problems, and to suggest a general algorithm. We also study the sensitivity analysis for these variational inequalities and complementarity problems using the projection technique. Several special cases are discussed, which can be obtained from our results.

A non-linear Goursat problem for a high order polyvibrating equation

1986 ◽  
Vol 102 (1-2) ◽  
pp. 159-172
Author(s):  
Andrzej Borzymowski
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Functional Equations ◽  
Goursat Problem ◽  
Common Point ◽  
Existence Of A Solution ◽  
Non Linear

SynopsisThis paper proves the existence of a solution of a non-linear Goursat problem for a partial differential equation of order 2p (p ≧ 2) with the boundary conditions given on 2p curves emanating from a common point. The problem is reduced to a system of integro-differential-functional equations and then Schauder's fixed point theorem is applied.

scholarly journals New approach to solutions of a class of singular fractional q-differential problem via quantum calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sihua Liang ◽  
Mohammad Esmael Samei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Present Article ◽  
Existence Of Solutions ◽  
Differential Problem ◽  
New Approach ◽  
Quantum Calculus ◽  
Non Linear ◽  
Linear Problems ◽  
Fixed Point Technique

AbstractIn the present article, by using the fixed point technique and the Arzelà–Ascoli theorem on cones, we wish to investigate the existence of solutions for a non-linear problems regular and singular fractional q-differential equation $$ \bigl({}^{c}D_{q}^{\alpha }f\bigr) (t) = w \bigl(t, f(t), f'(t), \bigl({}^{c}D_{q}^{ \beta }f \bigr) (t) \bigr), $$(cDqαf)(t)=w(t,f(t),f′(t),(cDqβf)(t)), under the conditions $f(0) = c_{1} f(1)$f(0)=c1f(1), $f'(0)= c_{2} ({}^{c}D_{q} ^{\beta } f) (1)$f′(0)=c2(cDqβf)(1) and $f''(0) = f'''(0) = \cdots =f^{(n-1)}(0) = 0$f″(0)=f‴(0)=⋯=f(n−1)(0)=0, where $\alpha \in (n-1, n)$α∈(n−1,n) with $n\geq 3$n≥3, $\beta , q \in J=(0,1)$β,q∈J=(0,1), $c_{1} \in J$c1∈J, $c_{2} \in (0, \varGamma _{q} (2- \beta ))$c2∈(0,Γq(2−β)), the function w is $L^{\kappa }$Lκ-Carathéodory, $w(t, x_{1}, x_{2}, x_{3})$w(t,x1,x2,x3) and may be singular and ${}^{c}D_{q}^{\alpha }$Dqαc the fractional Caputo type q-derivative. Of course, here we applied the definitions of the fractional q-derivative of Riemann–Liouville and Caputo type by presenting some examples with tables and algorithms; we will illustrate our results, too.

scholarly journals On nonlinear variational inequalities

1991 ◽  
Vol 14 (2) ◽  
pp. 399-402 ◽  
Author(s):  
Muhammed Aslam Noor
Keyword(s):  
Fixed Point ◽  
Approximate Solution ◽  
Variational Inequalities ◽  
Boundary Value Problems ◽  
Iterative Algorithm ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
Odd Order ◽  
Fixed Point Technique

The fixed point technique is used to prove the existence of a solution for a class of nonlinear variational inequalities related with odd order constrained boundary value problems and to suggest an iterative algorithm to compute the approximate solution.

scholarly journals Existence of a solution of fractional differential equations using the fixed point technique in extended $ b $-metric spaces

2021 ◽  
Vol 7 (1) ◽  
pp. 518-535
Author(s):  
Monica-Felicia Bota ◽  
◽  
Liliana Guran ◽  
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Fractional Operator ◽  
Integral Type ◽  
Existence Of A Solution ◽  
Fractional Differential ◽  
Fixed Point Technique ◽  
Cyclic Type

<abstract><p>The purpose of the present paper is to prove some fixed point results for cyclic-type operators in extended $ b $-metric spaces. The considered operators are generalized $ \varphi $-contractions and $ \alpha $-$ \varphi $ contractions. The last section is devoted to applications to integral type equations and nonlinear fractional differential equations using the Atangana-Bǎleanu fractional operator.</p></abstract>

CLASS OF BOOLEAN FUNCTIONS CONSTRUCTED USING SIGNIFICANT BITS OF LINEAR RECURRENCES OVER THE RING ℤ2n

2019 ◽  
Vol 6 (2) ◽  
pp. 90-94
Author(s):  
Hernandez Piloto Daniel Humberto
Keyword(s):  
Linear Function ◽  
Boolean Functions ◽  
Hamming Distance ◽  
Linear Recurrences ◽  
Maximum Period ◽  
Non Linear ◽  
The Given ◽  
Class Of Functions

In this work a class of functions is studied, which are built with the help of significant bits sequences on the ring ℤ2n. This class is built with use of a function ψ: ℤ2n → ℤ2. In public literature there are works in which ψ is a linear function. Here we will use a non-linear ψ function for this set. It is known that the period of a polynomial F in the ring ℤ2n is equal to T(mod 2)2α, where α∈ , n01- . The polynomials for which it is true that T(F) = T(F mod 2), in other words α = 0, are called marked polynomials. For our class we are going to use a polynomial with a maximum period as the characteristic polyomial. In the present work we show the bounds of the given class: non-linearity, the weight of the functions, the Hamming distance between functions. The Hamming distance between these functions and functions of other known classes is also given.

scholarly journals Existence of the Solutions of Nonlinear Fractional Differential Equations Using the Fixed Point Technique in Extended b-Metric Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 158
Author(s):  
Liliana Guran ◽  
Monica-Felicia Bota
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Boundary Value ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Existence Of A Solution ◽  
Shadowing Property ◽  
Limit Shadowing ◽  
Type Boundary ◽  
Cyclic Type

The purpose of this paper is to prove fixed point theorems for cyclic-type operators in extended b-metric spaces. The well-posedness of the fixed point problem and limit shadowing property are also discussed. Some examples are given in order to support our results, and the last part of the paper considers some applications of the main results. The first part of this section is devoted to the study of the existence of a solution to the boundary value problem. In the second part of this section, we study the existence of solutions to fractional boundary value problems with integral-type boundary conditions in the frame of some Caputo-type fractional operators.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

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