We establish the unique solvability of an inverse Cauchy problem for the equation utα-rtutβ+a2-∆γ/2u-btu=F0(x), x,t∈ℝn×(0,T]" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">, with fractional derivatives, given distributions F0" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: 400; font-size: 16.94px; letter-spacing: normal; overflow-wrap: normal; word-spacing: 0px; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; color: rgba(0, 0, 0, 0.87); font-family: "Noto Sans", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen-Sans, Ubuntu, Cantarell, "Helvetica Neue", sans-serif; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;"> and in right-hand sides of the initial conditions. The problem is to find the generalized solution u (continuous and integrable in time in generalized sense) and unknown continuous and integrable coefficients b(t), r(t).
- ACS Style
- Lopushanska, H.; Shumska, V.R. Finding the two youngest coefficients in the telegraph equation with fractional derivatives. Bukovinian Mathematical Journal. 2017, 4
- AMA Style
- Lopushanska H, Shumska VR. Finding the two youngest coefficients in the telegraph equation with fractional derivatives. Bukovinian Mathematical Journal. 2017; 4(3-4).
- Chicago/Turabian Style
- Halyna Lopushanska, Vitalia Romanivna Shumska. 2017. "Finding the two youngest coefficients in the telegraph equation with fractional derivatives". Bukovinian Mathematical Journal. 4 no. 3-4.