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New error bounds for Newton’s formula associated with tempered fractional integrals
In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error...
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On Grüss, Ostrowski and trapezoid-type inequalities via nabla integral on time scales
Ostrowski inequality gives the absolute deviation of the function from its integral mean. Delta and nabla calculi are first two approaches to study...
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Fractional Spectral and Fractional Finite Element Methods: A Comprehensive Review and Future Prospects
In this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe...
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On some investigations of alpha-conformable Ostrowski–Trapezoid–Grüss dynamic inequalities on time scales
We prove new Ostrowski-type α -conformable dynamic inequalities and its companion inequalities on time scales by using the integration-by-parts...
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Why Fractional Fuzzy
In many practical situation, control experts can only formulate their experience by using imprecise (“fuzzy”) words from natural language. To...
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On new Milne-type inequalities for fractional integrals
In this study, fractional versions of Milne-type inequalities are investigated for differentiable convex functions. We present Milne-type...
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Novel results of Milne-type inequalities involving tempered fractional integrals
In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of...
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Fractional Systems: Theoretical Foundations
An overview of the fractional order integro-differential, methods and tools of fractional calculus that are commonly used in control and automation...
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Calculation of Distributed-Order Fractional Derivative on Tensor Cores-Enabled GPU
Due to an increased computational complexity of calculating the values of the distributed-order Caputo fractional derivative compared to the...
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Some Riemann–Liouville fractional integral inequalities of corrected Euler–Maclaurin-type
In this research article, an equality is established for Riemann–Liouville fractional integral. With the help of this equality, some corrected...
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A novel fractional time-delayed grey model with discrete fractal derivative and its applications in predicting enrollments and educational expenditure
Accurate forecasting of the enrollment scale of higher education and education expenditure is the key to scientific decision-making in education....
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Fractional inequalities of corrected Euler–Maclaurin-type for twice-differentiable functions
In this article, an identity is proved for the case of twice-differentiable functions whose second derivatives in absolute value are convex. With the...
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Numerical framework for the Caputo time-fractional diffusion equation with fourth order derivative in space
A finite difference scheme along with a fourth-order approximation is examined in this article for finding the solution of time-fractional diffusion...
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Efficient alternating direction implicit numerical approaches for multi-dimensional distributed-order fractional integro differential problems
This paper proposes the alternating direction implicit (ADI) numerical approaches for computing the solution of multi-dimensional distributed-order...
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On the multiparameterized fractional multiplicative integral inequalities
We introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for...
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Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions
The distributed-order fractional telegraph models are commonly used to describe the phenomenas of diffusion and wave-like anomalous, which can model...
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A Fokker–Planck Equation with a Fractional Derivative Along the Trajectory of Motion with Conservation Law
AbstractThe paper presents a new mathematical model of the convection-diffusion process with ‘memory along the flow path’. It is described by...
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Numerical scheme for Erdélyi–Kober fractional diffusion equation using Galerkin–Hermite method
The aim of this work is to devise and analyse an accurate numerical scheme to solve Erdélyi–Kober fractional diffusion equation. This solution can be...
