Geodesic
On the solution of some higher-order integro-differential equations of special form
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 1, pp. 14-22

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The article is devoted to the solution of boundary value problems for higher-order linear integro-differential equations of Fredholm type with differential and integral operators encompassing powers of an ideal bijective linear differential operator whose inverse is known explicitly. The conditions for existence and uniqueness of solutions are derived and the solutions are delivered in closed form. The approach is based on the view that an integro-differential operator is a perturbed differential operator. The results obtained are of both theoretical and practical importance. The method is elucidated by solving two illustrative problems.
Keywords: integro-differential equations, initial value problems, boundary value problems, differential operators, power operators, composite products
Mots-clés : exact solutions. 
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     author = {E. Providas and I. N. Parasidis},
     title = {On the solution of some higher-order integro-differential equations of special form},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {14--22},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2020_26_1_a1/}
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E. Providas; I. N. Parasidis. On the solution of some higher-order integro-differential equations of special form. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 26 (2020) no. 1, pp. 14-22. http://geodesic.mathdoc.fr/item/VSGU_2020_26_1_a1/