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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
Turkish Journal of Mathematics
Using the coincidence degree theory of Mawhin and constructing appropriate operators, we investigate the existence of solutions to Hadamard fractional differential equations (FRDEs) at resonance { − (HDγu ) (t) = f(t, u(t)), t ∈ (1, e), u(1) = 0, u(e) = ∫ e 1 u(t)dA(t), where 1 < γ < 2, f : [1, e]×R2 → R satisfies Carathéodory conditions, ∫ e 1 u(t)dA(t) is the Riemann–Stieltjes integration, and (HDγu ) is the Hadamard fractional derivation of u of order γ . An example is included to illustrate our result.
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Turkish Journal of Mathematics
This paper establishes Lyapunov-type inequalities for a family of two-point $(\mathtt{n},\mathtt{p})$-type boundary value problems for Riemann-Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide a few examples, one of which is a fractional differential equation with delay.
Inverse Nodal Problems For Dirac Type Integro Differential System With A Nonlocal Boundary Condition, Baki̇ Keski̇n
Inverse Nodal Problems For Dirac Type Integro Differential System With A Nonlocal Boundary Condition, Baki̇ Keski̇n
Turkish Journal of Mathematics
In this paper, the Dirac type integro differential system\ with a nonlocal integral boundary condition is considered. First, we derive the asymptotic expressions for the solutions and large eigenvalues. Second, we provide asymptotic expressions for the nodal points and prove that a dense subset of nodal points uniquely determines the boundary condition parameter and the potential function of the considered differential system. We also provide an effective procedure for solving the inverse nodal problem.
A Third-Order P-Laplacian Boundary Value Problem On An Unbounded Domain, Samuel Azubuike Iyase, Ogbu Famous Imaga
A Third-Order P-Laplacian Boundary Value Problem On An Unbounded Domain, Samuel Azubuike Iyase, Ogbu Famous Imaga
Turkish Journal of Mathematics
In this work, we apply Leray-Schauder continuation principle to establish the existence of at least one solution to the third order p-Laplacian boundary value problem on an unbounded domain of the form \begin{equation*} (w(t) \varphi_{p}( u^{\prime\prime}(t)))^{\prime} = K ( t, u(t) , u^{\prime}(t), u^{\prime\prime}(t) ) , t \in ( 0, \infty) \end{equation*} \begin{equation*} u(0)= 0, \, u^{\prime} (0) = \sum^{m}_{i=1} \alpha _{i} \int_{0}^{\xi_{i}} u(t) dt, \, \lim_{t \rightarrow\infty} ( w(t)\varphi_{p} ( u^{\prime \prime} (t)) = 0 \end{equation*} under the nonresonant condition $ \sum_{i=1}^{m} \alpha_{i} \xi^{2} \neq 2. $
A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari
A New Implicit-Explicit Local Differential Method For Boundary Value Problems, Hüseyi̇n Tunç, Murat Sari
Turkish Journal of Mathematics
In this study, an effective numerical method based on Taylor expansions is presented for boundary value problems. This method is arbitrary directional and called as implicit-explicit local differential transform method (IELDTM). With the completion of this study, a reliable numerical method is derived by optimizing the required degrees of freedom. It is shown that the order refinement procedure of the IELDTM does not affect the degrees of freedom. A priori error analysis of the current method is constructed and order conditions are presented in a detailed analysis. The theoretical order expectations are verified for nonlinear BVPs. Stability of the IELDTM …
A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan
A Performance Assessment Of An Hdg Method For Second-Order Fredholm Integro-Differential Equation: Existence-Uniqueness And Approximation, Mehmet Fati̇h Karaaslan
Turkish Journal of Mathematics
In this paper, we obtain the existence--uniqueness of solution to the second-order linear Fredholm integro-differential equation (FIDE) with Dirichlet boundary condition by hybridizable discontinuous Galerkin (HDG) method. A key property of these methods is to eliminate all internal degrees of freedom and to construct a linear system that only includes globally coupled unknowns at the element interfaces. After designing and implementing HDG algorithm, we provide some necessary and sufficient conditions based on the stabilization parameter and kernel function to guarantee the existence-uniqueness of the approximate solution. Then, some numerical examples are carried out to assess the performance of the present …
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Existence Of Positive Solutions For Nonlinear Multipoint P-Laplacian Dynamic Equations On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we investigate the existence of positive solutions for nonlinear multipoint boundary value problems for p-Laplacian dynamic equations on time scales with the delta derivative of the nonlinear term. Sufficient assumptions are obtained for existence of at least twin or arbitrary even positive solutions to some boundary value problems. Our results are achieved by appealing to the fixed point theorems of Avery-Henderson. As an application, an example to demonstrate our results is given.
On A Nonnegativity Principle With Applications To A Certain Multitermfractional Boundary Value Problem, Noureddine Ferfar, Said Mazouzi
On A Nonnegativity Principle With Applications To A Certain Multitermfractional Boundary Value Problem, Noureddine Ferfar, Said Mazouzi
Turkish Journal of Mathematics
The main object of the present paper is to state and prove a general nonnegativity principle in the framework of multiterm fractional differential equations, which we use to investigate some iterative monotone sequences of lower and upper solutions to a certain fractional eigenvalue problem. The obtained results can be easily extended to fractional differential equations of distributed orders since the latter are the natural extension of multiterm fractional differential equations.
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal
Existence Of Solutions Of Bvps For Impulsive Fractional Langevin Equations Involving Caputo Fractional Derivatives, Yuji Liu, Ravi Agarwal
Turkish Journal of Mathematics
The standard Caputo fractional derivative is generalized for the piecewise continuous functions. A more general boundary value problem for the impulsive Langevin fractional differential equation involving the Caputo fractional derivatives is studied. New existence results for solutions of concerned problems are established.
Solvability Of Boundary Value Problems For Coupled Impulsive Differential Equations With One-Dimensional P-Laplacians, Yuji Liu
Turkish Journal of Mathematics
This paper is concerned with a boundary value problem of impulsive differential systems on the whole line with one-dimensional p-Laplacians. By constructing a weighted Banach space and defining a nonlinear operator, together with Schauder's fixed point theorem, sufficient conditions to guarantee the existence of at least one solution are established (Theorems 3.1-3.3). Two examples are given to illustrate the main results.
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$(\phi_p(x^\Delta(t)))^\nabla+w(t)f(t,x(t),x^\Delta(t))=0,\hspace{2cm} t_1< t 1.$ Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term $f$ is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.
Strong Solution For A High Order Boundary Value Problem With Integral Condition, Ahcene Merad, Ahmed Lakhdar Marhoune
Strong Solution For A High Order Boundary Value Problem With Integral Condition, Ahcene Merad, Ahmed Lakhdar Marhoune
Turkish Journal of Mathematics
The present paper is devoted to a proof of the existence and uniqueness of strong solution for a high order boundary value problem with integral condition. The proof is based by a priori estimate and on the density of the range of the operator generated by the studied problem.