We explore ovals of constant width in polar coordinates this paper. Conversion a parametric function defined on rectangular domain angles, to representation angles is introduced, and the relationship between discussed. The length curve opposite points from one vertex point next can be determined using oval’s vertices. A new verification Barbier's theorem presented. show that extreme values radial coordinate discussed oval are obtained at both its vertices points. Ovals specific circles with...

In this work, we suggest a new method for solving linear multi-term time-fractional wave-diffusion equations, which is named the modified fractional reduced differential transform (m-FRDTM). The importance of technique that it suggests solution equation. Very few techniques have been proposed to solve type equation, as will be shown in paper. To show effectiveness and efficiency method, introduce two different applications two-term equations. three-dimensional two-dimensional plots values...

Suitable spline functions of polynomial form are derived and used to solve linear nonlinear fractional differential equations. The proposed method is applicable for 0 < α ≤ 1 ≥ 1, where denotes the order derivative in Caputo sense. results obtained good agreement with exact analytical solutions numerical presented elsewhere. Results also show that technique introduced here robust easy apply.

In this study, exact and approximate solutions of higher-dimensional time-fractional diffusion equations were obtained using a relatively new method, the fractional reduced differential transform method (FRDTM). The can be found with benefit special function, we applied Caputo derivatives in method. numerical results graphical representations specified that proposed is very effective for solving higher dimensions.

In this paper, appropriate spline functions in polynomial form are outlined and applied to solve higher-order linear fractional differential equations (H-OLFDEs). Several techniques have been proposed type of equations. A description the projected methodology is first introduced. The method involves transforming H-OLFDE order α, with given initial conditions, into a system , denoting Caputo derivative for each equation i transformed system, where number resulting equal that conditions....

In this article, we study ovals of constant width in a plane, comparing them to particular circles. We use the vertices on oval, after counting them, as reference measure length curve between opposite points. A new proof Barbier’s theorem is introduced. distance function from origin points oval introduced, and it shown that extreme values occur at Comparisons are made prove differences distances circles small within certain range. also all types described paper analytically geometrically...