Abstract
In the present study, we dilate the differential transform scheme to develop a reliable scheme for studying analytically the mutual impact of temporal and spatial fractional derivatives in Caputo’s sense. We also provide a mathematical framework for the transformed equations of some fundamental functional forms in fractal 2-dimensional space. To demonstrate the effectiveness of our proposed scheme, we first provide an elegant scheme to estimate the (mixed-higher) Caputo-fractional derivatives, and then we give an analytical treatment for several (non)linear physical case studies in fractal 2-dimensional space. The study concluded that the proposed scheme is very efficacious and convenient in extracting solutions for wide physical applications endowed with two different memory parameters as well as in approximating fractional derivatives.
Acknowledgements
The work of the first, third and fourth authors was supported by the Deanship of Scientific Research at the University of Jordan.
References
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Solution of a Moving Boundary Problem for Soybean Hydration by Numerical Approximation
- Comparison between 2D and 3D Simulation of Contact of Two Deformable Axisymmetric Bodies
- Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals
- Soliton Solutions for Some Nonlinear Partial Differential Equations in Mathematical Physics Using He’s Variational Method
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- An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Solution of a Moving Boundary Problem for Soybean Hydration by Numerical Approximation
- Comparison between 2D and 3D Simulation of Contact of Two Deformable Axisymmetric Bodies
- Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals
- Soliton Solutions for Some Nonlinear Partial Differential Equations in Mathematical Physics Using He’s Variational Method
- Application of the Euler and Runge–Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors
- Dynamical Analysis of a Fractional-Order Hantavirus Infection Model
- An Avant-Garde Handling of Temporal-Spatial Fractional Physical Models
- Existence, Uniqueness and UHR Stability of Solutions to Nonlinear Ordinary Differential Equations with Noninstantaneous Impulses
- A Study on Impulsive Hilfer Fractional Evolution Equations with Nonlocal Conditions
- Unique Solution for Multi-point Fractional Integro-Differential Equations