Hi 

I forgot how to display the output ar an array i.e. (r,u(r)) (table of data)

I am sure i will find answers here.

a:=-0.1:alpha:=0.2:

dsys:={diff(u(r),r,r)+((1-alpha)/r+r^(alpha-2))*diff(u(r),r)=a};

res1:=dsolve(dsys union {u(0.05)=0,u(1)=0},numeric);

When a and b are from 0 to 1 it works!! but from -1 to -0.05 not i wonder why?

a1:=1.9:alpha:=0.2:
ode1 := diff( y(x), x$2 ) + x^(-1)* diff( y(x), x )  = 2*a1*(1+x^(2-alpha)/((2-alpha)^2*GAMMA(2-alpha))):
    bc1 := y(0)=subs(r=-0.05,a1/4*(r^2-1)), y(-1)=0:
a:=-1:b:=-0.05:
N := 20:h := (b-a)/N:
X := k -> a+k*h: 
'X'[k] = X(k):
Yp  := k -> (y[k+1]-y[k-1])/2/((1+alpha)*GAMMA(1+alpha)*h^(alpha)):Ypp := k -> (y[k+1]-2*y[k]+y[k-1])/((2-alpha)*GAMMA(2-alpha)*(h^(2-alpha))^2):
for k from 1 to N-1 do
eq[k] := eval( ode1,
                    {x=X(k), y(x)=y[k],
                     diff(y(x),x)=Yp(k),
                     diff(y(x),x$2)=Ypp(k)} ):
    end do:

eq[0] := y[0] = rhs(bc1[1]):
eq[N] := y[N] = rhs(bc1[2]):
    fd_sol1 := fsolve( {seq( eq[k], k=0..N )}, {seq( y[k], k=0..N )} ):
fd_table1 := eval( seq([X(k),y[k]],k=0..N), fd_sol1 ):Matrix([fd_table1]):
infolevel[dsolve] := 3:
#exact_sol1 := combine(dsolve( { ode1, bc1 }, y(x) )):
infolevel[dsolve] := 0:

P1:=plot([fd_table1], x=a..b,color=[black], linestyle = solid, symbolsize=16,axes=boxed);

Hi experts in the field of solving complex system of ODE

I have this sytem of var. are  (n(t),u(t),z(t)) with delta and t are (real)

then want to plot 3d n(t) as a function of( t, delta)

restart:assume(delta,real):
phi:=0:lambda:=0.1:N:=5:M:=sqrt(N*(N+1))*exp(I*phi):omegap:=10:
var:={n(t),u(t),z(t)}:
dsys:={diff(n(t),t)=-2*(n(t)-N)+(u(t)-M)*exp(-2*I*omegap*t/lambda)+((z(t)-conjugate(M))*exp(2*I*omegap*t/lambda)),diff(u(t),t)=-2*(1-I*delta)*u(t)+2*(n(t)-N)*exp(2*I*omegap*t/lambda)+2*M,diff((z(t),t))=-2*(1+I*delta)*z(t)+2*(n(t)-N)*exp(-2*I*omegap*t/lambda)+2*conjugate(M)}:
res1:=dsolve(dsys union {n(0)=0,u(0)=0,z(0)=0},numeric,output=listprocedure);

P3:=plots3d(n(t),t=0..1,delta=-10..10,axes=boxed,tickmarks = [3, 2], color = black, thickness = 1, linestyle = solid, titlefont = [Helvetica, roman, 18], labeldirections = [horizontal, vertical], labelfont = [Helvetica, roman, 24]);

Hi Mapke experts,Here is my try to solve the integration

int(x-t)^(-alpha)*a(t-bln(t+b/b),t from 0 to x)

I found it complicated to solve it symbolic, so \i try this:

restart:
assume(t,real):
x[0]:=0:a:=-0.1:alpha:=0.5:h:=0.001:b:=Gamma(2-alpha)/((1-alpha)*Gamma(1-alpha)):
for n from 0 to 0 do
t[n]:=n*h:
vo:=a*(x[n]-b*(ln((x[n]+b)/b))):
uo:=a*(t[n]-b*(ln((t[n]+b)/b))):
u1:=(int((x[n]-t[n])^(-alpha)*uo,t[n]=0..x[n])):
S[n]:=vo+u1:
od:

data:=[seq([t[n],S[n]],n=0..100)]:

Here the code for BVP, but there is a singularity how to avoid it

a:=-0.1:alpha:=0.1:
dsys:={diff(u(r),r,r)+(1-alpha)/r+r^(alpha-2)*diff(u(r),r)=a};

res1:=dsolve(dsys union {u(-1)=0,u(1)=0},numeric,output=listprocedure);

plots[odeplot](res1,[[r,(u(r))]],-5..5,axes=boxed,tickmarks = [3, 2], color = black, thickness = 1, linestyle = solid, titlefont = [Helvetica, roman, 18], labeldirections = [horizontal, vertical], labelfont = [Helvetica, roman, 24]);