in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

In 32PO4-labeled adipocytes, isoproterenol (ISO) or physiologically relevant concentrations of insulin rapidly increased phosphorylation of a particulate 135-kDa protein which has been identified as a cGMP-inhibited "low Km" cAMP phosphodiesterase (CGI-PDE) by several criteria, including selective immunoprecipitation with anti-CGI-PDE IgG (Degerman, E., Smith, C.J., Tornqvist, H., Vasta, V., Be...

PDE surfaces, whose behavior is governed by Partial Differential Equations (PDEs), have demonstrated many modeling advantages in surface blending, free-form surface modeling, and surface’s aesthetic or functional specifications. Although PDE surfaces can potentially unify geometric attributes and functional constraints for surface design, current PDE-based techniques exhibit certain difficultie...

The purpose of this paper to explain the role and importance fractional derivatives for mass heat transfer in Casson nanofluids including clay nanoparticles. These particles can be found water, kerosene, engine oil. physical flow phenomena are illustrated using PDE thermophysical nanoparticle properties, addresses fluid along with chemical reaction generation. fluxes generalized constant propor...

In applied sciences and engineering, partial differential equations (PDE) of integer non-integer order play a crucial role. It can be challenging to determine these equations’ exact solutions. As result, developing numerical approaches obtain precise solutions kinds takes time. The homotopy perturbation transform method (HPTM) Yang decomposition (YTDM) are the subjects several recent findings t...

Gaussian curvature is an important geometric property of surfaces, which has been used broadly in mathematical modeling. Due to the full nonlinearity curvature, efficient numerical methods for models based on it are uncommon literature. In this article, we propose operator-splitting method a general model. our method, decouple from differential operators by introducing two matrix- and vector-va...

This paper is devoted to the numerical computation of algebraic linear systems involving several matrix power functions; that finding x solution $$\sum _{\alpha \in \mathbb {R}}A^{\alpha }x=b$$ . These will be referred as Generalized Fractional Algebraic Linear Systems (GFALS). In this paper, we derive gradient methods for solving these very computationally complex problems, which themselves re...

<p style='text-indent:20px;'>We prove higher Sobolev regularity for bounded weak solutions to a class of nonlinear nonlocal integro-differential equations. The leading operator exhibits nonuniform growth, switching between two different fractional elliptic "phases" that are determined by the zero set modulating coefficient. Solutions shown improve both in integrability and differentiabili...