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On the variable-order fractional derivatives with respect to another function
In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and...
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Calculus of variations with higher order Caputo fractional derivatives
In this work, we consider fractional variational problems depending on higher order fractional derivatives. We obtain optimality conditions for such...
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Enhanced shifted Jacobi operational matrices of derivatives: spectral algorithm for solving multiterm variable-order fractional differential equations
This paper presents a new way to solve numerically multiterm variable-order fractional differential equations (MTVOFDEs) with initial conditions by...
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Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time
A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the...
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A comparative study for mathematical modelling of the contest of CAR-T and tumour cells in solid cancers using fractional- and integer-order derivatives
Cancer is a disease resulting from the fractious growth and division of abnormal cells and has gotten consistent and dedicated attention from...
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On the order reduction of approximations of fractional derivatives: an explanation and a cure
Finite-difference based approaches are common for approximating the Caputo fractional derivative. Often, these methods lead to a reduction of the...
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Asymptotic behavior of fractional-order nonlinear systems with two different derivatives
This paper addresses the asymptotic behavior of systems described by nonlinear differential equations with two fractional derivatives. Using the...
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High Order Numerical Scheme for Generalized Fractional Diffusion Equations
In this paper, a higher order finite difference scheme is proposed for generalized fractional diffusion equations (GFDEs). The fractional diffusion...
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Extended dissipative performance of fractional-order neural networks via LMI approach
This paper investigates the extended dissipativity performance of a specific category of fractional-order neural networks. The derivatives involving...
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On variable-order fractional linear viscoelasticity
A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing...
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Qualitative Analysis of Fractional Stochastic Differential Equations with Variable Order Fractional Derivative
This research paper has been dedicated to the investigation of Coupled System of Fractional Stochastic Differential Equations (CSFSDEs), which is an...
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Fractional-order rat bite fever model: a mathematical investigation into the transmission dynamics
The fractional ordered mathematical model offers more insights compared to integer order models. In this work, we analyzed fractional order rat bite...
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Approximate Solutions of Third-Order Time Fractional Dispersive Equations with Singular and Nonsingular Kernel Derivatives
The natural transform decomposition method (NTDM) is an effective analytical method that combines the Adomian decomposition method (ADM) and the...
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Minimax Solutions of Homogeneous Hamilton–Jacobi Equations with Fractional-Order Coinvariant Derivatives
The Cauchy problem is considered for a homogeneous Hamilton–Jacobi equation with fractional-order coinvariant derivatives, which arises in problems...
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A numerical approach based on Vieta–Fibonacci polynomials to solve fractional order advection–reaction diffusion problem
In this article, we attempt to provide the numerical solution for a non-linear reaction--advection diffusion equation with fractional-order...
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Inverse Problem for a Third-Order Parabolic-Hyperbolic Equation Involves Fractional Derivatives
AbstractIn this article the questions of unique solvability of inverse problem for a third order parabolic-hyperbolic type equation with Caputo...
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Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints
This paper investigates nonsmooth multiobjective fractional programming (NMFP) with inequalities and equalities constraints in real reflexive Banach...
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Treatment of fractional multi-order/multi-term differential equations: utilizing fractional shifted Lucas polynomials
In this work, novel type of fractional polynomials are proposed as the generalization to shifted Lucas polynomials, which are called as fractional...
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Variable-Order Fractional Laplacian and its Accurate and Efficient Computations with Meshfree Methods
The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical...
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Higher order numerical methods for fractional delay differential equations
In this paper, we present a new family of higher-order numerical methods for solving non-linear fractional delay differential equations (FDDEs) along...
