Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval
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DOI: 10.1002/mma.4106
Abstract: In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval D0+αu(t)+ft,u(t),D0+α−1u(t)=0,t∈(0,+∞), with the integral boundary conditions u(0)=0,D0+α−1u(∞)=∫0τg1(s)u(s)ds+a,D0+α−2u(0)=∫0τg2(s)u(s)ds+b. By using Krasnoselskii fixed point theorem, the existence results of positive solutions… read more here.
Keywords: infinite interval; positive solutions; integral boundary; fractional differential ... See more keywords
Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
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DOI: 10.1002/mma.4617
Abstract: R. Almeida was supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia), within project… read more here.
Keywords: respect kernel; equations caputo; caputo derivative; fractional differential ... See more keywords
Fractional differential and integral operations via cumulative approach
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DOI: 10.1002/mma.5450
Abstract: In this study, a fractal operator model of cumulative processes is described. Accordingly, differential and integral operators of the fractional calculus are derived by the fractal operator model of a cumulative process. In order to… read more here.
Keywords: integral operations; differential integral; approach fractional; cumulative approach ... See more keywords
On positive solutions of fractional differential equations with change of sign
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DOI: 10.1002/mma.5619
Abstract: We study the existence and uniqueness of positive solutions of fractional differential equations with change of sign D0+α(u′′(t))=h(t)f(u(t)),0 read more here.
Keywords: change sign; solutions fractional; positive solutions; equations change ... See more keywords
An efficient numerical method for nonlinear fractional differential equations based on the generalized Mittag‐Leffler functions and Lagrange polynomials
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DOI: 10.1002/mma.6852
Abstract: In this paper, an efficient numerical method is developed for solving a class of nonlinear fractional differential equations. The main idea is to transform the nonlinear fractional differential equations into a system of integral equations… read more here.
Keywords: nonlinear fractional; numerical method; method; fractional differential ... See more keywords
S-Asymptotically $$\varvec{\omega }$$ω-Periodic Mild Solutions of Neutral Fractional Differential Equations with Finite Delay in Banach Space
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DOI: 10.1007/s00009-017-0855-4
Abstract: In this paper, we present some results concerning the existence and uniqueness of S-asymptotically $$\omega $$ω-periodic solutions for a class of nonlinear fractional differential equations with finite delay in Banach space X. These results are… read more here.
Keywords: delay banach; equations finite; fractional differential; omega periodic ... See more keywords
On Hyers–Ulam Stability for Fractional Differential Equations Including the New Caputo–Fabrizio Fractional Derivative
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DOI: 10.1007/s00009-019-1407-x
Abstract: In this paper, we study the stability in the sense of Hyers–Ulam for the following fractional differential equations including the new Caputo–Fabrizio fractional derivative: $$\begin{aligned} \left( ^{CF}D^{\alpha }y\right) \left( x\right) =f\left( x\right) \quad \qquad \quad… read more here.
Keywords: left right; including new; equations including; fractional differential ... See more keywords
Constructive Existence of Solutions of Multi-point Boundary Value Problem for Hilfer Fractional Differential Equation at Resonance
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DOI: 10.1007/s00009-020-01512-8
Abstract: In this paper, we study the constructive existence of solutions of multi-point boundary value problem for Hilfer fractional differential equation at resonance. The constructive existence of solutions is very important in practice, because it gives… read more here.
Keywords: value; value problem; fractional differential; hilfer fractional ... See more keywords
Existence and Asymptotic Behavior of Positive Solutions for a Coupled System of Semilinear Fractional Differential Equations
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DOI: 10.1007/s00025-016-0528-9
Abstract: In this paper, we study a coupled system of semilinear Riemann–Liouville type fractional differential equations. Applying the Schäuder fixed point theorem, we prove the existence of positive solutions of the fractional differential system. Furthermore, the… read more here.
Keywords: system; positive solutions; system semilinear; fractional differential ... See more keywords
Spectral collocation method for nonlinear Riemann–Liouville fractional differential system
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DOI: 10.1007/s10092-021-00403-y
Abstract: The spectral collocation method is investigated for the system of nonlinear Riemann–Liouville fractional differential equations (FDEs). The main idea of the presented method is to solve the corresponding system of nonlinear weakly singular Volterra integral… read more here.
Keywords: system; fractional differential; liouville fractional; riemann liouville ... See more keywords
High-Order Accurate Adaptive Kernel Compression Time-Stepping Schemes for Fractional Differential Equations
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DOI: 10.1007/s10915-017-0393-z
Abstract: High-order adaptive methods for fractional differential equations are proposed. The methods rely on a kernel compression scheme for the approximation and localization of the history term. To avoid complications typical to multistep methods, we focus… read more here.
Keywords: order; high order; fractional differential; differential equations ... See more keywords