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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 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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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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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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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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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...
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Piecewise Fractional Interpolation with Application to Fractional Differential Equation
In this paper, we introduce a new family of interpolants, called piecewise fractional interpolants (PFIs). The proposed interpolants are used to...
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Decomposition and conformal map** techniques for the quadrature of nearly singular integrals
Gauss–Legendre quadrature, Clenshaw–Curtis quadrature and the trapezoid rule are powerful tools for numerical integration of analytic functions. For...
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Convergence Analysis of a Finite Volume Scheme for a Distributed Order Diffusion Equation
We consider a distributed order diffusion equation with space-dependent conductivity. The distributed order operator is defined via an integral of...
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Some parameterized inequalities by means of fractional integrals with exponential kernels and their applications
We use the definition of a new class of fractional integral operators, recently introduced by Ahmad et al. in [J. Comput. Appl. Math. 353:120–129,
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Determination of the Fractional Order in Semilinear Subdiffusion Equations
We analyze the inverse boundary value-problem to determine the fractional order ν of nonautonomous semilinear subdiffusion equations with memory...
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Efficient shifted fractional trapezoidal rule for subdiffusion problems with nonsmooth solutions on uniform meshes
This article devotes to develo** robust and simple correction techniques with efficient algorithms for a class of second-order time step**...
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On Some Hermite–Hadamard Inequalities for Fractional Integrals and their Applications
We establish some new extensions of Hermite–Hadamard inequality for fractional integrals and present several applications for the Beta-function.