Study of Caputo fractional derivative and Riemann–Liouville integral with different orders and its application in multi‐term differential equations
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DOI: 10.1002/mma.10392
Abstract: In this article, we initially provided the relationship between the RL fractional integral and the Caputo fractional derivative of different orders. Additionally, it is clear from the literature that studies into boundary value problems involving… read more here.
Keywords: multi term; caputo fractional; differential equations; fractional derivative ... See more keywords
A numerical‐analytical solution of multi‐term fractional‐order differential equations
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DOI: 10.1002/mma.6242
Abstract: In this paper, a solution to initial value problems for fractional‐order linear commensurate multi‐term differential equations with Caputo derivatives is presented. The solution is obtained in the form of a finite sum of the Mittag‐Leffler–type… read more here.
Keywords: numerical analytical; fractional order; solution; multi term ... See more keywords
Legendre multiwavelet functions for numerical solution of multi-term time-space convection–diffusion equations of fractional order
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DOI: 10.1007/s00366-019-00896-w
Abstract: In this study, the Ritz–Galerkin method based on Legendre multiwavelet functions is introduced to solve multi-term time-space convection–diffusion equations of fractional order with variable coefficients and initial-boundary conditions. This method reduces the problem to a… read more here.
Keywords: time space; space convection; term time; multiwavelet functions ... See more keywords
Mixed finite-element method for multi-term time-fractional diffusion and diffusion-wave equations
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DOI: 10.1007/s40314-017-0447-8
Abstract: In this paper, numerical theory based on the mixed finite-element method and finite difference analog of the Caputo fractional derivative for multi-term time-fractional diffusion equations and diffusion-wave equations is analyzed. The unconditional stability and convergence… read more here.
Keywords: finite element; diffusion; mixed finite; element method ... See more keywords
Approximate Solution for a Fuzzy Fractional Multi-term Differential Equation by Müntz Polynomials
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DOI: 10.1007/s40819-021-00988-6
Abstract: In this study, we present a new approach for the numerical solution of a fuzzy fractional multi term differential equation under the Caputo fractional derivative which orders in [0, 1]. To do this, collocation method based… read more here.
Keywords: fuzzy fractional; differential equation; solution fuzzy; term differential ... See more keywords
Stability analysis of multi-term fractional-differential equations with three fractional derivatives
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124751
Abstract: Abstract Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases, fractional-order-dependent as well as fractional-order-independent characterisations of stability… read more here.
Keywords: term fractional; fractional differential; differential equations; stability ... See more keywords
Efficient computational hybrid method for the solution of 2D multi-term fractional order advection-diffusion equation
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DOI: 10.1088/1402-4896/ad4d28
Abstract: Multi-term time-fractional advection diffusion equations are vital for simulating a wide range of physical phenomena, including fluid dynamics and environmental transport processes. However, due to their natural complexity, these equations pose challenges for conventional numerical… read more here.
Keywords: multi term; method; advection diffusion;
Finite difference scheme for multi-term variable-order fractional diffusion equation
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DOI: 10.1186/s13662-018-1544-8
Abstract: In this paper, we consider a multi-term variable-order fractional diffusion equation on a finite domain, which involves the Caputo variable-order time fractional derivative of order α(x,t)∈(0,1)$\alpha(x,t) \in(0,1) $ and the Riesz variable-order space fractional derivatives… read more here.
Keywords: difference; order; multi term; order fractional ... See more keywords
Some applications and maximum principles for multi-term time-space fractional parabolic Monge-Ampère equation
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DOI: 10.1515/dema-2024-0031
Abstract: Abstract This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère operator and the multi-term time-space fractional Caputo-Fabrizio derivative. Based on the maximum principle established above, on the one hand, we show… read more here.
Keywords: multi term; time space; monge amp; term time ... See more keywords
Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms
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DOI: 10.1515/fca-2018-0019
Abstract: Abstract In this paper, we consider the analytical solutions of multi-term time-space fractional partial differential equations with nonlocal damping terms for general mixed Robin boundary conditions on a finite domain. Firstly, method of reduction to… read more here.
Keywords: analytical solutions; multi term; differential equations; term time ... See more keywords
A numerical study for solving multi-term fractional-order differential equations
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DOI: 10.2298/tsci23s1401n
Abstract: In this article, we extended operational matrices using orthonormal Boubaker polynomials of Riemann-Liouville fractional integration and Caputo derivative to find numerical solution of multi-term fractional-order differential equations (FDE). The proposed method is utilized to convert… read more here.
Keywords: term fractional; order differential; differential equations; fractional order ... See more keywords