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Fractional Dissipative PDEs
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their...
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A comparative study of fractional derivatives to interpret wave structures for the higher order fractional Ramani equation
This study investigates wave solutions to the higher order Ramani equation with beta derivative via the generalized Kudryashov and the extended...
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Studying the impacts of M-fractional and beta derivatives on the nonlinear fractional model
The major goal of the current research is to investigate the effects of fractional parameters on the dynamic response of soliton waves of fractional...
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Solution of the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives in statistical mechanics
AbstractWe solve the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives for systems exhibiting noninteger power laws...
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Numerical Methods for Fractional PDEs
Numerical approaches for the computation of fractional derivatives on the whole real line (also called the fractional Laplacian) are discussed....
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On the soliton solutions to the density-dependent space time fractional reaction–diffusion equation with conformable and M-truncated derivatives
In this manuscript, the density-dependent space-time fractional reaction–diffusion equation in the sense of conformable and M-truncated derivatives...
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Comparison of fractional effects for Phi-4 equation using beta and M-truncated derivatives
Fractional Phi -4 equation plays a crucial role in many studies of nuclear and particle physics. In this paper, the fractional Phi -4 equation is...
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Fractional Derivative Models
Models that are described by the differential equations with the derivatives of the fractional order are considered including the fractional Fourier...
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Modeling and analysis of an implicit fractional order differential equation with multiple first-order fractional derivatives and non-local boundary conditions
In recent years, researchers have investigated boundary value problems of single terms and, in rare circumstances, multi-term fractional differential...
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The space–time-fractional derivatives order effect of Caputo–Fabrizio on the do** profiles for formation a p-n junction
AbstractIn this study, we treated the space–time-fractional diffusion equation in a semi-infinite medium using a recently developed fractional...
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Optical soliton solutions of fractional Sasa-Satsuma equation with beta and conformable derivatives
In this paper, the optical soliton and other solutions of fractional Sasa-Satsuma equation are investigated with fractional beta derivative and...
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Soliton solutions for the time-fractional nonlinear differential-difference equation with conformable derivatives in the ferroelectric materials
The ultimate focus of this research is to provide soliton solutions to the nonlinear differential-difference equations via conformable fractional...
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Fractional Wave Models and Their Experimental Applications
A focused summary of one- and two-dimensional models for linear and nonlinear wave propagation in fractional media is given. The basic models, which...
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Extended Lie symmetry approach for mixed fractional derivatives of magneto-electro-elastic circular rod: innovative reduction, conservation laws, optical solitons and bifurcation analysis
The central objective of this study is to examine how the Lie symmetry technique and conservation law theories can be employed to analyze fractional...
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On the optical soliton solutions of time-fractional Biswas–Arshed equation including the beta or M-truncated derivatives
This article investigates the optical soliton solutions of the time-fractional Biswas–Arshed (BA) equation, which is a new model for soliton...
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A study on fractional HBV model through singular and non-singular derivatives
The current study’s aim is to evaluate the dynamics of a Hepatitis B virus (HBV) model with the class of asymptomatic carriers using two different...
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Solitons to the time-fractional Radhakrishnan–Kundu–Lakshmanan equation with \(\beta\) and M-truncated fractional derivatives: a comparative analysis
In this study, the dynamics of perturbed fractional Radhakrishnan–Kundu–Lakshman (RKL) equation is investigated taking the fractional derivatives as
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Fractional Integrable Dispersive Equations
Fractional equations arise widely in physical systems and nonlinear integrable systems are fundamentally important in the study of nonlinear...
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Fractional optical normalization operator of magnetic field and electroosmotic optimistic energy
In this manuscript, we introduce optical fractional normalization and fractional recursive operators for a particle. The significance of this...
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Comparison of Caputo and Atangana–Baleanu fractional derivatives for the pseudohyperbolic telegraph differential equations
In this paper, numerical solution of partial differential equations of the so-called hyperbolic telegraph, which has different applications in many...
