On the uniqueness of solutions of Volterra equations

A Kneser-Type Theorem for an Integral Equation in Locally Convex Spaces

“…Hence s))ds for t G J. o ^ ~ Applying Theorem 1 with a = 1 -r and theorem on integral inequalities ( [2], Lemma 1) from this we deduce that v(t) = 0 for t G J. Thus P p (V(t)) = 0 for t G J and p G P. Therefore for each t G J the set V(t) is relatively compact in E. As the set V is equicontinuous, Ascoli's theorem proves that V is relatively compact in C. Hence the sequence (u n ) has a limit point u.…”

Several Results of Fractional Differential and Integral Equations in Distribution

“…For example, Gorenflo and Mainardi [7] provided interesting applications of Abel's integral equations of the first and second kind in solving the partial differential equation which describes the problem of the heating (or cooling) of a semi-infinite rod by influx (or efflux) of heat across the boundary into (or from) its interior. There have been lots of approaches, including numerical analysis, thus far to studying fractional differential and integral equations, including Abel's equations, with many applications [8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Recently, Li et al [22,23] studied integral equations associated with Abel's types in the distributional (Schwartz) sense, based on new fractional calculus of distributions and derived fresh results which are not achievable in the classical sense.…”

Solutions to Abel’s Integral Equations in Distributions

“…The development of integral equations has led to the construction of many real world problems, such as mathematical physics models [23,24], scattering in quantum mechanics and water waves. There have been lots of techniques, such as numerical analysis and integral transforms [25][26][27], thus far to studying fractional differential and integral equations, including Abel's equations, with many applications [1,20,[28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”