Time‐Dependent Term Identification in the Time–Space Fractional Derivative Diffusion Equation From Integral Over Specified Condition
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Publication Date
Wed Jul 01 2020
Journal Name
Journal Of Physics: Conference Series
A Multilevel Approach for Stability Conditions in Fractional Time Diffusion Problems
Abstract<p>The Caputo definition of fractional derivatives introduces solution to the difficulties appears in the numerical treatment of differential equations due its consistency in differentiating constant functions. In the same time the memory and hereditary behaviors of the time fractional order derivatives (TFODE) still common in all definitions of fractional derivatives. The use of properties of companion matrices appears in reformulating multilevel schemes as generalized two level schemes is employed with the Gerschgorin disc theorems to prove stability condition. Caputo fractional derivatives with finite difference representations is considered. Moreover the effect of using the inverse operator which tr</p>
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Publication Date
Thu Jan 01 2015
Journal Name
Finite Difference Methods,theory And Applications
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Publication Date
Sun Apr 30 2023
Journal Name
Iraqi Journal Of Science
Numerical and Analytical Solutions of Space-Time Fractional Partial Differential Equations by Using a New Double Integral Transform Method
This work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.
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Publication Date
Thu Oct 01 2015
Journal Name
Applied Mathematics And Computation
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Publication Date
Fri Jan 01 2016
Journal Name
Applied Numerical Mathematics
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Publication Date
Mon May 01 2017
Journal Name
Applied Mathematics And Computation
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Publication Date
Thu Feb 01 2018
Journal Name
Applied Mathematical Modelling
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Publication Date
Mon Jan 01 2024
Journal Name
Results In Nonlinear Analysis
Publication Date
Tue Feb 10 2026
Journal Name
F1000research
Simultaneous Numerical Determination of Two Time-dependent Coefficients in Second Order Parabolic Equation With Nonlocal Initial and Boundary Conditions
Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine
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Publication Date
Thu Dec 21 2023
Journal Name
Mathematical Modelling Of Engineering Problems
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