Fractional Calculus and Shannon Wavelet

<table>Fractional derivative of the function <svg height="23.825001" id="M209" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 55.387501 23.825001" width="55.387501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,19.325)"><path d="M556 393q0 -39 -36 -106q-42 -78 -185 -279q-47 -66 -81 -108t-117 -135l-112 -26l-8 22q150 90 251 219q-6 136 -39 340q-8 53 -21 53q-6 0 -27 -19.5t-38 -42.5l-16 26q80 111 127 111q23 0 35 -28t20 -90q18 -137 27 -263h2q142 200 142 279q0 24 -14 48q-4 7 5 26
q13 28 43 28q18 0 30 -15.5t12 -39.5z" id="x1D466"></path></g><g transform="matrix(.017,-0,0,-.017,14.613,19.325)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,29.317,19.325)"><path d="M391 364q0 -28 -20.5 -53.5t-50 -43.5t-70 -34t-73.5 -25t-68 -17v-29q0 -48 20 -81t65 -33q73 0 157 76l16 -23q-107 -113 -221 -113q-21 0 -40.5 6.5t-39 22t-31.5 47t-12 75.5q0 69 33.5 139.5t95.5 114.5q77 55 143 55q42 0 69 -24.5t27 -59.5zM313 350
q0 26 -14.5 40.5t-37.5 14.5q-32 0 -44 -7q-82 -46 -104 -175q200 49 200 127z" id="x1D452"></path></g>
<g transform="matrix(.012,-0,0,-.012,36.363,11.175)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.012,-0,0,-.012,43.347,11.175)"><use xlink:href="#x1D465"></use></g>
<g transform="matrix(.008,-0,0,-.008,50,5.463)"><use xlink:href="#x32"></use></g>
</svg> with upper limit <svg height="11.3125" id="M210" style="vertical-align:-0.1092pt" version="1.1" viewbox="0 0 42.5625 11.3125" width="42.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.113)"><use xlink:href="#x1D441"></use></g><g transform="matrix(.017,-0,0,-.017,19.628,11.113)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,34.332,11.113)"><use xlink:href="#x34"></use></g>
</svg> at different values of <svg height="14.85" id="M211" style="vertical-align:-2.22495pt" version="1.1" viewbox="0 0 171.7375 14.85" width="171.7375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><use xlink:href="#x1D708"></use></g><g transform="matrix(.017,-0,0,-.017,13.814,12.012)"><use xlink:href="#x3D"></use></g><g transform="matrix(.017,-0,0,-.017,28.518,12.012)"><use xlink:href="#x30"></use></g><g transform="matrix(.017,-0,0,-.017,36.678,12.012)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,43.392,12.012)"><use xlink:href="#x31"></use></g><g transform="matrix(.017,-0,0,-.017,51.552,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,58.555,12.012)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,66.715,12.012)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,73.412,12.012)"><use xlink:href="#x32"></use></g><g transform="matrix(.017,-0,0,-.017,81.572,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,88.575,12.012)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,96.734,12.012)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,103.449,12.012)"><use xlink:href="#x33"></use></g><g transform="matrix(.017,-0,0,-.017,111.608,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,118.612,12.012)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,126.771,12.012)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,133.486,12.012)"><use xlink:href="#x34"></use></g><g transform="matrix(.017,-0,0,-.017,141.645,12.012)"><use xlink:href="#x2F"></use></g><g transform="matrix(.017,-0,0,-.017,148.649,12.012)"><use xlink:href="#x35"></use></g><g transform="matrix(.017,-0,0,-.017,156.808,12.012)"><use xlink:href="#x2C"></use></g><g transform="matrix(.017,-0,0,-.017,163.505,12.012)"><use xlink:href="#x31"></use></g>
</svg>. </table>

Mathematical Problems in Engineering

Fractional Calculus and Shannon Wavelet

Figure 6