A k

We investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii’s fixed point theorem. We present an example in order to illustrate our results

Positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary conditions

We study the existence and uniqueness of positive solutions for a sum-type singular fractional integro-differential equation with m-point boundary condition. Also, we provide an example to illustrate our main result.Publisher's Versio

The existence and numerical solution for a k-dimensional system of multi-term fractional integro-differential equations

First, we investigate the existence and uniqueness of solution for a k-dimensional system of multi-term fractional integro-differential equations. Also, we apply shifted Chebyshev and shifted Legendre polynomials to obtain an approximation solution for the k-dimensional system. Finally, we provide some examples illustrating the presented methods

The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems

We discuss the existence of positive solutions for the coupled system of multiterm singular fractional integrodifferential boundary value problems D0+αu(t)+f1(t,u(t),v(t),(ϕ1u)(t),(ψ1v)(t),D0+pu(t),D0+μ1v(t),D0+μ2v(t),…,D0+μmv(t))=0,D0+βv(t)+f2(t,u(t),v(t),(ϕ2u)(t),(ψ2v)(t),D0+qv(t),D0+ν1u(t),D0+ν2u(t),…,D0+νmu(t))=0, u(i)(0)=0 and v(i)(0)=0 for all 0≤i≤n-2, [D0+δ1u(t)]t=1=0 for 2<δ1<n-1 and α-δ1≥1, [D0+δ2v(t)]t=1=0 for 2<δ2<n-1 and β-δ2≥1, where n≥4, n-1<α,β<n, 0<p,q<1, 1<μi,νi<2  (i=1,2,…,m), γj,λj:[0,1]×[0,1]→(0,∞) are continuous functions (j=1,2) and (ϕju)(t)=∫0t‍γj(t,s)u(s)ds,(ψjv)(t)=∫0t‍λj(t,s)v(s)ds. Here D is the standard Riemann-Liouville fractional derivative, fj  (j=1,2) is a Caratheodory function, and fj(t,x,y,z,w,v,u1,u2,…,um) is singular at the value 0 of its variables

On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions

On the Ulam-Hyers-Rassias stability of two structures of discrete fractional three-point boundary value problems: existence theory

We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville and Caputo fractional derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle and the Brouwer fixed point criterion. Moreover, we prove stability, including Hyers-Ulam and Hyers-Ulam-Rassias type results. Finally, some numerical models are provided to illustrate and validate the theoretical results.The Portuguese Foundation for Science and Technology (FCT) and CIDMA. NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation.publishe

2-Absorbing Vague Weakly Complete Γ-Ideals in Γ-Rings

The aim of this study is to provide a generalization of prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing vague weakly complete Γ-ideals of commutative Γ-rings. A novel algebraic structure of a primary vague Γ-ideal of a commutative Γ-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Γ-ideals of Γ-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Γ-ideals and 2-absorbing Γ-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Γ-ideal of a Γ-ring and 2-absorbing K-vague Γ-ideal of a Γ-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Γ-ring of R induced by a 2-absorbing vague weakly complete Γ-ideal of a 2-absorbing Γ-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Γ-ideal