Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
8 results
Search Results
Article Quasilinear Coupled System in the Frame of Nonsingular Abc-Derivatives With P-Laplacian Operator at Resonance(Springer Basel Ag, 2024) Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; Bouloudene, MokhtarWe investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana-Baleanu-Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge's application of Mawhin's continuation theorem. Examples are provided to demonstrate our findings.Article Citation - WoS: 14Citation - Scopus: 14Boundary Value Problem of Weighted Fractional Derivative of a Function With a Respect To Another Function of Variable Order(Springer, 2023) Jarad, Fahd; Alqudah, Manar A.; Abdeljawad, Thabet; Benia, Kheireddine; Souid, Mohammed SaidThis study aims to resolve weighted fractional operators of variable order in specific spaces. We establish an investigation on a boundary value problem of weighted fractional derivative of one function with respect to another variable order function. It is essential to keep in mind that the symmetry of a transformation for differential equations is connected to local solvability, which is synonymous with the existence of solutions. As a consequence, existence requirements for weighted fractional derivative of a function with respect to another function of constant order are necessary. Moreover, the stability with in Ulam-Hyers-Rassias sense is reviewed. The outcomes are derived using the Kuratowski measure of non-compactness. A model illustrates the trustworthiness of the observed results.Article Citation - WoS: 10Citation - Scopus: 11Optimal Variational Iteration Method for Parametric Boundary Value Problem(Amer inst Mathematical Sciences-aims, 2022) Nadeem, Muhammad; Karim, Shazia; Akguel, Ali; Jarad, Fahd; Ain, Qura Tul; Akgül, AliMathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.Article Citation - WoS: 2Citation - Scopus: 4A New Application of the Legendre Reproducing Kernel Method(Amer inst Mathematical Sciences-aims, 2022) Hashemi, Mir Sajjad; Gholizadeh, Leila; Akgul, Ali; Jarad, Fahd; Foroutan, Mohammad RezaIn this work, we apply the reproducing kernel method to coupled system of second and fourth order boundary value problems. We construct a novel algorithm to acquire the numerical results of the nonlinear boundary-value problems. We also use the Legendre polynomials. Additionally, we discuss the convergence analysis and error estimates. We demonstrate the numerical simulations to prove the efficiency of the presented method.Article Citation - WoS: 5Citation - Scopus: 3Nonlinear Fractional Differential Equations and Their Existence Via Fixed Point Theory Concerning To Hilfer Generalized Proportional Fractional Derivative(Amer inst Mathematical Sciences-aims, 2022) Ahmad, Abdulaziz Garba; Jarad, Fahd; Alsaadi, Ateq; Rashid, SaimaThis article adopts a class of nonlinear fractional differential equation associating Hilfer generalized proportional fractional (GPF) derivative with having boundary conditions, which amalgamates the Riemann-Liouville (RL) and Caputo-GPF derivative. Taking into consideration the weighted space continuous mappings, we first derive a corresponding integral for the specified boundary value problem. Also, we investigate the existence consequences for a certain problem with a new unified formulation considering the minimal suppositions on nonlinear mapping. Detailed developments hold in the analysis and are dependent on diverse tools involving Schauder's, Schaefer's and Kransnoselskii's fixed point theorems. Finally, we deliver two examples to check the efficiency of the proposed scheme.Article Citation - WoS: 15Citation - Scopus: 18A Study of Symmetric Contractions With an Application To Generalized Fractional Differential Equations(Springer, 2021) Karapinar, Erdal; Hussain, Aftab; Jarad, FahdThis article proposes four distinct kinds of symmetric contraction in the framework of complete F-metric spaces. We examine the condition to guarantee the existence and uniqueness of a fixed point for these contractions. As an application, we look for the solutions to fractional boundary value problems involving a generalized fractional derivative known as the fractional derivative with respect to another function.Article Citation - WoS: 36Citation - Scopus: 44Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives(Springer, 2018) Jarad, Fahd; Ozbekler, Abdullah; Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, JehadWe state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.Article Citation - WoS: 71Citation - Scopus: 94A Generalized Lyapunov-Type Inequality in the Frame of Conformable Derivatives(Springeropen, 2017) Abdeljawad, Thabet; Alzabut, Jehad; Jarad, FahdWe prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) = 0, t is an element of (c, d), x(c) = x(d) = 0 has a nontrivial solution, where r is a real-valued continuous function on [c, d], then integral(d)(c) vertical bar r(t)vertical bar dt > alpha(alpha)/(alpha - 1)(alpha-1) (d - c)(a-1). (1) Moreover, a Lyapunov type inequality of the form integral(d)(c)vertical bar r(t)vertical bar dt > 3 alpha - 1/(d - c)(2 alpha-1) (3 alpha - 1/2 alpha - 1)(2 alpha-1/a), 1/2 < alpha <= 1, (2) is obtained for a sequential conformable BVP. Some examples are given and an application to conformable Sturm-Liouville eigenvalue problem is analyzed.